यदि \(A=\{1,2,3,5\}\) और \(B=\{2,4,5,6\}\) हैं, तो \(A\cup B\) क्या होगा?
If \(A=\{1,2,3,5\}\) and \(B=\{2,4,5,6\}\), what is \(A\cup B\)?
#sets
#union
#basic-operation
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A ( {1,2,3,4,5,6} )
B ( {2,5} )
C ( {1,3} )
D ( {4,6} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,4,5,6} )
Step 1
Concept
\(A\cup B\) contains all distinct elements of both sets. In exams, write repeated elements only once.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,4,5,6} ). \(A\cup B\) contains all distinct elements of both sets. In exams, write repeated elements only once.
Step 3
Exam Tip
\(A\cup B\) में दोनों समुच्चयों के सभी अलग-अलग अवयव आते हैं। परीक्षा में दोहराए गए अवयव केवल एक बार लिखें।
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यदि \(A={x:x\in\mathbb{N},2\mid x,x\le16}\) और \(B={x:x\in\mathbb{N},4\mid x,x\le16}\) हैं, तो \(A\setminus B\) क्या है?
If \(A={x:x\in\mathbb{N},2\mid x,x\le16}\) and \(B={x:x\in\mathbb{N},4\mid x,x\le16}\), what is \(A\setminus B\)?
#sets
#difference
#multiples
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A ( {2,6,10,14} )
B ( {4,8,12,16} )
C ( {2,4,6,8,10,12,14,16} )
D \( \emptyset \)
Explanation opens after your attempt
Correct Answer
A. ( {2,6,10,14} )
Step 1
Concept
(A) has even natural numbers up to (16), and (B) has multiples of (4). Hence \(A\setminus B={2,6,10,14}\).
Step 2
Why this answer is correct
The correct answer is A. ( {2,6,10,14} ). (A) has even natural numbers up to (16), and (B) has multiples of (4). Hence \(A\setminus B={2,6,10,14}\).
Step 3
Exam Tip
(A) में (16) तक के सम धन पूर्णांक हैं और (B) में (4) के गुणज हैं। इसलिए \(A\setminus B={2,6,10,14}\) है।
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यदि \(A=\{3,6,9,12\}\) और \(B=\{6,12,18\}\) हैं, तो \(A\cap B\) ज्ञात कीजिए।
If \(A=\{3,6,9,12\}\) and \(B=\{6,12,18\}\), find \(A\cap B\).
#sets
#intersection
#common-elements
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A ( {3,9} )
B ( {6,12} )
C ( {3,6,9,12,18} )
D ( {18} )
Explanation opens after your attempt
Correct Answer
B. ( {6,12} )
Step 1
Concept
\(A\cap B\) contains only elements common to both sets. Carefully pick the shared elements.
Step 2
Why this answer is correct
The correct answer is B. ( {6,12} ). \(A\cap B\) contains only elements common to both sets. Carefully pick the shared elements.
Step 3
Exam Tip
\(A\cap B\) में केवल वे अवयव आते हैं जो दोनों में समान हों। साझा अवयवों को ध्यान से छांटना चाहिए।
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यदि \(A\cup B=A\) और \(A\cap B=B\) है, तो सही संबंध कौन सा है?
If \(A\cup B=A\) and \(A\cap B=B\), which relation is correct?
#sets
#subset
#union-intersection
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A \(B\subseteq A\)
B \(A\subseteq B\)
C \(A=B=\emptyset\)
D \(A\cap B=\emptyset\)
Explanation opens after your attempt
Correct Answer
A. \(B\subseteq A\)
Step 1
Concept
Both conditions show that every element of (B) is in (A). Therefore \(B\subseteq A\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(B\subseteq A\). Both conditions show that every element of (B) is in (A). Therefore \(B\subseteq A\) is correct.
Step 3
Exam Tip
दोनों स्थितियां बताती हैं कि (B) के सभी अवयव (A) में हैं। इसलिए \(B\subseteq A\) सही है।
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यदि \(A=\{1,4,7,10\}\) और \(B=\{4,10,13\}\) हैं, तो \(A\setminus B\) क्या है?
If \(A=\{1,4,7,10\}\) and \(B=\{4,10,13\}\), what is \(A\setminus B\)?
#sets
#difference
#set-minus
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A ( {1,7} )
B ( {4,10} )
C ( {13} )
D ( {1,4,7,10,13} )
Explanation opens after your attempt
Correct Answer
A. ( {1,7} )
Step 1
Concept
\(A\setminus B\) contains elements of (A) that are not in (B). The difference may change when the order changes.
Step 2
Why this answer is correct
The correct answer is A. ( {1,7} ). \(A\setminus B\) contains elements of (A) that are not in (B). The difference may change when the order changes.
Step 3
Exam Tip
\(A\setminus B\) में (A) के वे अवयव आते हैं जो (B) में नहीं हैं। क्रम बदलने पर अंतर बदल सकता है।
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यदि (n\(A\setminus B\)=18), (n\(B\setminus A\)=14) और (n\(A\cap B\)=9) है, तो (n\(A\cup B\)) कितना होगा?
If (n\(A\setminus B\)=18), (n\(B\setminus A\)=14), and (n\(A\cap B\)=9), what is (n\(A\cup B\))?
#sets
#cardinality
#venn-diagram
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A (23)
B (32)
C (41)
D (50)
Explanation opens after your attempt
Step 1
Concept
The union is made from three disjoint parts \(A\setminus B\), \(B\setminus A\), and \(A\cap B\). Thus (18+14+9=41).
Step 2
Why this answer is correct
The correct answer is C. (41). The union is made from three disjoint parts \(A\setminus B\), \(B\setminus A\), and \(A\cap B\). Thus (18+14+9=41).
Step 3
Exam Tip
संघ तीन असंबद्ध भागों \(A\setminus B\), \(B\setminus A\) और \(A\cap B\) से बनता है। अतः (18+14+9=41)।
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यदि \(A=\{2,5,8,11\}\) और \(B=\{1,5,8,14\}\) हैं, तो \(B\setminus A\) कौन सा है?
If \(A=\{2,5,8,11\}\) and \(B=\{1,5,8,14\}\), which is \(B\setminus A\)?
#sets
#difference
#order-sensitive
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A ( {2,11} )
B ( {5,8} )
C ( {1,14} )
D ( {1,2,5,8,11,14} )
Explanation opens after your attempt
Correct Answer
C. ( {1,14} )
Step 1
Concept
\(B\setminus A\) keeps elements of (B) that are not in (A). Pay special attention to the first set.
Step 2
Why this answer is correct
The correct answer is C. ( {1,14} ). \(B\setminus A\) keeps elements of (B) that are not in (A). Pay special attention to the first set.
Step 3
Exam Tip
\(B\setminus A\) में (B) के ऐसे अवयव रहेंगे जो (A) में नहीं हैं। पहले लिखे समुच्चय पर विशेष ध्यान दें।
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यदि \(A=\{1,2,3,4,5,6,7\}\), \(B=\{2,4,6,8\}\) और \(C=\{1,4,7,10\}\) हैं, तो (\(A\setminus B\)\cap C) क्या है?
If \(A=\{1,2,3,4,5,6,7\}\), \(B=\{2,4,6,8\}\), and \(C=\{1,4,7,10\}\), what is (\(A\setminus B\)\cap C)?
#sets
#mixed-operation
#difference-intersection
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A ( {1,7} )
B ( {4} )
C ( {1,3,5,7} )
D ( {2,6,8,10} )
Explanation opens after your attempt
Correct Answer
A. ( {1,7} )
Step 1
Concept
First \(A\setminus B={1,3,5,7}\). Its intersection with (C) is ({1,7}).
Step 2
Why this answer is correct
The correct answer is A. ( {1,7} ). First \(A\setminus B={1,3,5,7}\). Its intersection with (C) is ({1,7}).
Step 3
Exam Tip
पहले \(A\setminus B={1,3,5,7}\) मिलता है। इसका (C) से प्रतिच्छेद ({1,7}) है।
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यदि \(A={x:x\in\mathbb{Z},-3\le x\le2}\) और \(B={x:x\in\mathbb{Z},x^2\le4}\) हैं, तो \(A\cup B\) क्या है?
If \(A={x:x\in\mathbb{Z},-3\le x\le2}\) and \(B={x:x\in\mathbb{Z},x^2\le4}\), what is \(A\cup B\)?
#sets
#integers
#union
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A ( {-3,-2,-1,0,1,2} )
B ( {-2,-1,0,1,2} )
C ( {-3,3} )
D ( {-1,0,1} )
Explanation opens after your attempt
Correct Answer
A. ( {-3,-2,-1,0,1,2} )
Step 1
Concept
\(A=\{-3,-2,-1,0,1,2\}\) and \(B=\{-2,-1,0,1,2\}\). Therefore \(A\cup B=A\).
Step 2
Why this answer is correct
The correct answer is A. ( {-3,-2,-1,0,1,2} ). \(A=\{-3,-2,-1,0,1,2\}\) and \(B=\{-2,-1,0,1,2\}\). Therefore \(A\cup B=A\).
Step 3
Exam Tip
\(A=\{-3,-2,-1,0,1,2\}\) और \(B=\{-2,-1,0,1,2\}\) है। इसलिए \(A\cup B=A\) है।
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यदि \(A=\{a,b,c,d\}\) और \(B=\{c,d,e,f\}\) हैं, तो (\(A\cup B\)\setminus \(A\cap B\)) क्या होगा?
If \(A=\{a,b,c,d\}\) and \(B=\{c,d,e,f\}\), what is (\(A\cup B\)\setminus \(A\cap B\))?
#sets
#union
#intersection
#difference
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A ( {a,b,e,f} )
B ( {c,d} )
C ( {a,b,c,d,e,f} )
D \( \emptyset \)
Explanation opens after your attempt
Correct Answer
A. ( {a,b,e,f} )
Step 1
Concept
\(A\cup B={a,b,c,d,e,f}\) and \(A\cap B={c,d}\), so the remaining elements are (a,b,e,f). This is a symmetric-difference type pattern.
Step 2
Why this answer is correct
The correct answer is A. ( {a,b,e,f} ). \(A\cup B={a,b,c,d,e,f}\) and \(A\cap B={c,d}\), so the remaining elements are (a,b,e,f). This is a symmetric-difference type pattern.
Step 3
Exam Tip
\(A\cup B={a,b,c,d,e,f}\) और \(A\cap B={c,d}\), इसलिए शेष (a,b,e,f) हैं। यह सममित अंतर जैसा पैटर्न है।
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यदि \(A\cap B={3,5}\), \(A\setminus B={1,7}\) और \(B\setminus A={2,9}\) है, तो (A) क्या होगा?
If \(A\cap B={3,5}\), \(A\setminus B={1,7}\), and \(B\setminus A={2,9}\), what is (A)?
#sets
#venn-parts
#set-formation
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A ( {1,3,5,7} )
B ( {2,3,5,9} )
C ( {1,2,3,5,7,9} )
D ( {3,5} )
Explanation opens after your attempt
Correct Answer
A. ( {1,3,5,7} )
Step 1
Concept
Set (A) contains both parts \(A\setminus B\) and \(A\cap B\). Hence \(A=\{1,3,5,7\}\).
Step 2
Why this answer is correct
The correct answer is A. ( {1,3,5,7} ). Set (A) contains both parts \(A\setminus B\) and \(A\cap B\). Hence \(A=\{1,3,5,7\}\).
Step 3
Exam Tip
समुच्चय (A) में \(A\setminus B\) और \(A\cap B\) दोनों भाग आते हैं। इसलिए \(A=\{1,3,5,7\}\) है।
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यदि \(A=\{2,3,4,5\}\) और \(B=\{4,5,6,7\}\) हैं, तो कौन सा कथन असत्य है?
If \(A=\{2,3,4,5\}\) and \(B=\{4,5,6,7\}\), which statement is false?
#sets
#false-statement
#difference
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A \(A\cap B={4,5}\)
B \(A\cup B={2,3,4,5,6,7}\)
C \(A\setminus B={2,3}\)
D \(B\setminus A={2,3}\)
Explanation opens after your attempt
Correct Answer
D. \(B\setminus A={2,3}\)
Step 1
Concept
\(B\setminus A\) contains elements of (B) that are not in (A), namely ({6,7}). In difference, changing order changes the answer.
Step 2
Why this answer is correct
The correct answer is D. \(B\setminus A={2,3}\). \(B\setminus A\) contains elements of (B) that are not in (A), namely ({6,7}). In difference, changing order changes the answer.
Step 3
Exam Tip
\(B\setminus A\) में (B) के वे अवयव होंगे जो (A) में नहीं हैं, यानी ({6,7})। अंतर में क्रम बदलने से उत्तर बदलता है।
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यदि \(A=\{1,2,3\}\) है, तो \(A\cup \emptyset\) क्या है?
If \(A=\{1,2,3\}\), what is \(A\cup \emptyset\)?
#sets
#empty-set
#union-identity
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A \( \emptyset \)
B ( {1,2,3} )
C ( {0,1,2,3} )
D ( {1,2} )
Explanation opens after your attempt
Correct Answer
B. ( {1,2,3} )
Step 1
Concept
The empty set has no element, so union with it does not change (A). Remember the identity law \(A\cup \emptyset=A\).
Step 2
Why this answer is correct
The correct answer is B. ( {1,2,3} ). The empty set has no element, so union with it does not change (A). Remember the identity law \(A\cup \emptyset=A\).
Step 3
Exam Tip
रिक्त समुच्चय में कोई अवयव नहीं होता, इसलिए संघ लेने पर (A) नहीं बदलता। पहचान नियम \(A\cup \emptyset=A\) याद रखें।
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यदि \(A=\{4,5,6\}\) है, तो \(A\cap \emptyset\) क्या है?
If \(A=\{4,5,6\}\), what is \(A\cap \emptyset\)?
#sets
#empty-set
#intersection
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A (A)
B ( {4,5,6} )
C \( \emptyset \)
D ( {0} )
Explanation opens after your attempt
Correct Answer
C. \( \emptyset \)
Step 1
Concept
There can be no common element in \(A\cap \emptyset\). Therefore the answer is always \(\emptyset\).
Step 2
Why this answer is correct
The correct answer is C. \( \emptyset \). There can be no common element in \(A\cap \emptyset\). Therefore the answer is always \(\emptyset\).
Step 3
Exam Tip
\(A\cap \emptyset\) में कोई सामान्य अवयव नहीं हो सकता। इसलिए उत्तर हमेशा \(\emptyset\) होता है।
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यदि (n(A)=18), (n(B)=12) और (n\(A\cap B\)=5) है, तो (n\(A\cup B\)) क्या है?
If (n(A)=18), (n(B)=12), and (n\(A\cap B\)=5), what is (n\(A\cup B\))?
#sets
#cardinality
#union-formula
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A (25)
B (30)
C (35)
D (23)
Explanation opens after your attempt
Step 1
Concept
Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). Thus (18+12-5=25).
Step 2
Why this answer is correct
The correct answer is A. (25). Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). Thus (18+12-5=25).
Step 3
Exam Tip
सूत्र (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)) लगाएं। इसलिए (18+12-5=25)।
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किसी कक्षा में (28) विद्यार्थी हिंदी, (22) अंग्रेजी और (10) दोनों पढ़ते हैं। हिंदी या अंग्रेजी पढ़ने वाले विद्यार्थियों की संख्या क्या है?
In a class, (28) students study Hindi, (22) study English, and (10) study both. How many students study Hindi or English?
#sets
#word-problem
#union
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A (40)
B (50)
C (60)
D (16)
Explanation opens after your attempt
Step 1
Concept
This is a question of (n\(A\cup B\)), so (28+22-10=40). Do not count students studying both twice.
Step 2
Why this answer is correct
The correct answer is A. (40). This is a question of (n\(A\cup B\)), so (28+22-10=40). Do not count students studying both twice.
Step 3
Exam Tip
यह (n\(A\cup B\)) का प्रश्न है, इसलिए (28+22-10=40)। दोनों पढ़ने वालों को दो बार न गिनें।
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यदि (n(A)=35), (n(B)=27) और (n\(A\cup B\)=50) है, तो (n\(A\cap B\)) कितना है?
If (n(A)=35), (n(B)=27), and (n\(A\cup B\)=50), what is (n\(A\cap B\))?
#sets
#cardinality
#intersection
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A (12)
B (8)
C (15)
D (20)
Explanation opens after your attempt
Step 1
Concept
By the formula, (n\(A\cap B\)=35+27-50=12). When union is given, find the common part using the formula.
Step 2
Why this answer is correct
The correct answer is A. (12). By the formula, (n\(A\cap B\)=35+27-50=12). When union is given, find the common part using the formula.
Step 3
Exam Tip
सूत्र से (n\(A\cap B\)=35+27-50=12)। संघ ज्ञात हो तो सामान्य भाग घटाकर नहीं बल्कि सूत्र से निकालें।
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यदि (n(A)=20) और (n\(A\setminus B\)=13) है, तो (n\(A\cap B\)) क्या होगा?
If (n(A)=20) and (n\(A\setminus B\)=13), what is (n\(A\cap B\))?
#sets
#difference
#cardinality
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A (7)
B (13)
C (20)
D (33)
Explanation opens after your attempt
Step 1
Concept
(A) is divided into \(A\setminus B\) and \(A\cap B\). Therefore (n\(A\cap B\)=20-13=7).
Step 2
Why this answer is correct
The correct answer is A. (7). (A) is divided into \(A\setminus B\) and \(A\cap B\). Therefore (n\(A\cap B\)=20-13=7).
Step 3
Exam Tip
(A) दो भागों \(A\setminus B\) और \(A\cap B\) में बंटता है। इसलिए (n\(A\cap B\)=20-13=7)।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,3,5,7\}\) और \(B=\{2,3,5,8\}\) हैं, तो \(A\cup B\) क्या है?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,3,5,7\}\), and \(B=\{2,3,5,8\}\), what is \(A\cup B\)?
#sets
#universal-set
#union
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A ( {1,2,3,5,7,8} )
B ( {3,5} )
C ( {4,6} )
D ( {1,7} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,5,7,8} )
Step 1
Concept
The union contains all distinct elements of (A) and (B). (U) only shows the universal boundary.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,5,7,8} ). The union contains all distinct elements of (A) and (B). (U) only shows the universal boundary.
Step 3
Exam Tip
संघ में (A) और (B) के सभी अलग-अलग अवयव शामिल होते हैं। (U) केवल सार्वत्रिक सीमा बताता है।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,4,8\}\) और \(B=\{2,4,6,8\}\) हैं, तो \(A\setminus B\) क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,4,8\}\), and \(B=\{2,4,6,8\}\), what is \(A\setminus B\)?
#sets
#difference
#finite-sets
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A ( {1} )
B ( {6} )
C ( {2,4,8} )
D ( {1,6} )
Explanation opens after your attempt
Correct Answer
A. ( {1} )
Step 1
Concept
In \(A\setminus B\), common elements of (B) are removed from (A). Removing (2,4,8) leaves (1).
Step 2
Why this answer is correct
The correct answer is A. ( {1} ). In \(A\setminus B\), common elements of (B) are removed from (A). Removing (2,4,8) leaves (1).
Step 3
Exam Tip
\(A\setminus B\) में (A) से (B) के समान अवयव हटाए जाते हैं। (2,4,8) हटाने पर (1) बचता है।
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यदि \(A\cap B=\emptyset\) है, तो (A) और (B) को क्या कहा जाता है?
If \(A\cap B=\emptyset\), what are (A) and (B) called?
#sets
#disjoint
#intersection
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A असंबद्ध समुच्चय / Disjoint sets
B बराबर समुच्चय / Equal sets
C उपसमुच्चय / Subsets
D सार्वत्रिक समुच्चय / Universal sets
Explanation opens after your attempt
Correct Answer
A. असंबद्ध समुच्चय / Disjoint sets
Step 1
Concept
If two sets have no common element, they are called disjoint sets. Understand \(\emptyset\) as having no element.
Step 2
Why this answer is correct
The correct answer is A. असंबद्ध समुच्चय / Disjoint sets. If two sets have no common element, they are called disjoint sets. Understand \(\emptyset\) as having no element.
Step 3
Exam Tip
यदि दो समुच्चयों में कोई सामान्य अवयव नहीं है, तो वे असंबद्ध कहलाते हैं। प्रतीक \(\emptyset\) को शून्य अवयव समझें।
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यदि \(A={x:x\in \mathbb{Z},-2\le x\le 3}\) और \(B={x:x\in \mathbb{Z},0\le x\le 5}\) हैं, तो \(A\cap B\) क्या है?
If \(A={x:x\in \mathbb{Z},-2\le x\le 3}\) and \(B={x:x\in \mathbb{Z},0\le x\le 5}\), what is \(A\cap B\)?
#sets
#integers
#intersection
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A ( {-2,-1,0,1,2,3} )
B ( {0,1,2,3} )
C ( {4,5} )
D ( {-2,-1,4,5} )
Explanation opens after your attempt
Correct Answer
B. ( {0,1,2,3} )
Step 1
Concept
The common integers in both intervals are (0,1,2,3). It is useful to convert inequalities into roster form first.
Step 2
Why this answer is correct
The correct answer is B. ( {0,1,2,3} ). The common integers in both intervals are (0,1,2,3). It is useful to convert inequalities into roster form first.
Step 3
Exam Tip
दोनों अंतरालों में समान पूर्णांक (0,1,2,3) हैं। असमानताओं को पहले सूची रूप में बदलना उपयोगी है।
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\(यदि (A={x:x\in \mathbb{N},x \le 10,x\) is prime\(}) और (B={x:x\in \mathbb{N},x \le 10,x\) is odd\(}) हैं, तो (A\setminus B) क्या है\)?
\(If (A={x:x\in \mathbb{N},x \le 10,x\) is prime\(}) and (B={x:x\in \mathbb{N},x \le 10,x\) is odd\(}), what is (A\setminus B)\)?
#sets
#prime-numbers
#difference
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A ( {2} )
B ( {3,5,7} )
C ( {1,3,5,7,9} )
D \( \emptyset \)
Explanation opens after your attempt
Correct Answer
A. ( {2} )
Step 1
Concept
\(A=\{2,3,5,7\}\) and \(B=\{1,3,5,7,9\}\), so \(A\setminus B={2}\). Remember that (1) is not prime.
Step 2
Why this answer is correct
The correct answer is A. ( {2} ). \(A=\{2,3,5,7\}\) and \(B=\{1,3,5,7,9\}\), so \(A\setminus B={2}\). Remember that (1) is not prime.
Step 3
Exam Tip
\(A=\{2,3,5,7\}\) और \(B=\{1,3,5,7,9\}\), इसलिए \(A\setminus B={2}\)। (1) अभाज्य नहीं है।
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\(यदि (A={x:x\) is a multiple of \(3,x\le 15}) और (B={x:x\) is a multiple of \(5,x\le 15}) हैं, तो (A\cup B) क्या है\)?
\(If (A={x:x\) is a multiple of \(3,x\le 15}) and (B={x:x\) is a multiple of \(5,x\le 15}), what is (A\cup B)\)?
#sets
#multiples
#union
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A ( {3,5,6,9,10,12,15} )
B ( {15} )
C ( {3,6,9,12} )
D ( {5,10,15} )
Explanation opens after your attempt
Correct Answer
A. ( {3,5,6,9,10,12,15} )
Step 1
Concept
\(A=\{3,6,9,12,15\}\) and \(B=\{5,10,15\}\), so the union has all distinct elements. Write (15) only once.
Step 2
Why this answer is correct
The correct answer is A. ( {3,5,6,9,10,12,15} ). \(A=\{3,6,9,12,15\}\) and \(B=\{5,10,15\}\), so the union has all distinct elements. Write (15) only once.
Step 3
Exam Tip
\(A=\{3,6,9,12,15\}\) और \(B=\{5,10,15\}\), इसलिए संघ में सभी अलग-अलग अवयव हैं। (15) को एक बार लिखें।
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यदि \(A=\{p,q,r,s\}\), \(B=\{r,s,t\}\) और \(C=\{s,t,u\}\) हैं, तो (A\cap \(B\cup C\)) क्या है?
If \(A=\{p,q,r,s\}\), \(B=\{r,s,t\}\), and \(C=\{s,t,u\}\), what is (A\cap \(B\cup C\))?
#sets
#three-sets
#intersection-union
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A ( {r,s} )
B ( {p,q} )
C ( {s,t} )
D ( {p,q,r,s,t,u} )
Explanation opens after your attempt
Correct Answer
A. ( {r,s} )
Step 1
Concept
First take \(B\cup C={r,s,t,u}\), then common elements with (A) are (r,s). Solve the bracket first.
Step 2
Why this answer is correct
The correct answer is A. ( {r,s} ). First take \(B\cup C={r,s,t,u}\), then common elements with (A) are (r,s). Solve the bracket first.
Step 3
Exam Tip
पहले \(B\cup C={r,s,t,u}\) लें, फिर (A) से सामान्य अवयव (r,s) मिलते हैं। कोष्ठक पहले हल करें।
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यदि \(A=\{1,2,3,4,5\}\), \(B=\{2,4,6\}\) और \(C=\{1,4,7\}\) हैं, तो (A\setminus \(B\cup C\)) क्या है?
If \(A=\{1,2,3,4,5\}\), \(B=\{2,4,6\}\), and \(C=\{1,4,7\}\), what is (A\setminus \(B\cup C\))?
#sets
#difference
#three-sets
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A ( {3,5} )
B ( {1,2,4} )
C ( {6,7} )
D ( {1,2,3,4,5,6,7} )
Explanation opens after your attempt
Correct Answer
A. ( {3,5} )
Step 1
Concept
\(B\cup C={1,2,4,6,7}\), so removing (1,2,4) from (A) leaves (3,5). In difference, only elements of the first set can remain.
Step 2
Why this answer is correct
The correct answer is A. ( {3,5} ). \(B\cup C={1,2,4,6,7}\), so removing (1,2,4) from (A) leaves (3,5). In difference, only elements of the first set can remain.
Step 3
Exam Tip
\(B\cup C={1,2,4,6,7}\), इसलिए (A) से (1,2,4) हटाने पर (3,5) बचते हैं। अंतर में केवल पहले समुच्चय के अवयव बचते हैं।
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कौन सा नियम (A\cap \(B\cup C\)=\(A\cap B\)\cup \(A\cap C\)) को दर्शाता है?
Which law is represented by (A\cap \(B\cup C\)=\(A\cap B\)\cup \(A\cap C\))?
#sets
#laws
#distributive-law
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A वितरण नियम / Distributive law
B क्रमविनिमेय नियम / Commutative law
C साहचर्य नियम / Associative law
D पूरक नियम / Complement law
Explanation opens after your attempt
Correct Answer
A. वितरण नियम / Distributive law
Step 1
Concept
This is distribution of intersection over union. To remember the name, notice how the bracket opens.
Step 2
Why this answer is correct
The correct answer is A. वितरण नियम / Distributive law. This is distribution of intersection over union. To remember the name, notice how the bracket opens.
Step 3
Exam Tip
यह प्रतिच्छेद का संघ पर वितरण है। नाम याद करने के लिए कोष्ठक खुलने जैसा पैटर्न देखें।
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यदि \(A=\{1,2\}\), \(B=\{2,3\}\) और \(C=\{3,4\}\) हैं, तो (\(A\cup B\)\cap C) क्या है?
If \(A=\{1,2\}\), \(B=\{2,3\}\), and \(C=\{3,4\}\), what is (\(A\cup B\)\cap C)?
#sets
#mixed-operation
#three-sets
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A ( {3} )
B ( {2} )
C ( {1,2,3,4} )
D \( \emptyset \)
Explanation opens after your attempt
Correct Answer
A. ( {3} )
Step 1
Concept
\(A\cup B={1,2,3}\) and its common part with (C) is (3). Order is very important in mixed operations.
Step 2
Why this answer is correct
The correct answer is A. ( {3} ). \(A\cup B={1,2,3}\) and its common part with (C) is (3). Order is very important in mixed operations.
Step 3
Exam Tip
\(A\cup B={1,2,3}\) और इसका (C) से सामान्य भाग (3) है। मिश्रित क्रियाओं में क्रम बहुत महत्वपूर्ण है।
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यदि \(A=\{2,3,5,7\}\), \(B=\{1,3,5,9\}\) और \(C=\{3,4,5\}\) हैं, तो (\(A\cap B\)\cup C) क्या है?
If \(A=\{2,3,5,7\}\), \(B=\{1,3,5,9\}\), and \(C=\{3,4,5\}\), what is (\(A\cap B\)\cup C)?
#sets
#mixed-operation
#union-intersection
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A ( {3,5} )
B ( {3,4,5} )
C ( {2,3,4,5,7} )
D ( {1,2,3,4,5,7,9} )
Explanation opens after your attempt
Correct Answer
B. ( {3,4,5} )
Step 1
Concept
\(A\cap B={3,5}\), and union with (C) gives ( {3,4,5} ). Find the bracket result first.
Step 2
Why this answer is correct
The correct answer is B. ( {3,4,5} ). \(A\cap B={3,5}\), and union with (C) gives ( {3,4,5} ). Find the bracket result first.
Step 3
Exam Tip
\(A\cap B={3,5}\), और (C) से संघ लेने पर ( {3,4,5} ) मिलता है। पहले कोष्ठक का परिणाम निकालें।
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यदि \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6\}\) हैं, तो (\(A\setminus B\)\cup \(B\setminus A\)) क्या है?
If \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), what is (\(A\setminus B\)\cup \(B\setminus A\))?
#sets
#symmetric-difference
#difference
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A ( {1,2,5,6} )
B ( {3,4} )
C ( {1,2,3,4,5,6} )
D \( \emptyset \)
Explanation opens after your attempt
Correct Answer
A. ( {1,2,5,6} )
Step 1
Concept
\(A\setminus B={1,2}\) and \(B\setminus A={5,6}\), so the union is ({1,2,5,6}). It joins the non-common parts of both sets.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,5,6} ). \(A\setminus B={1,2}\) and \(B\setminus A={5,6}\), so the union is ({1,2,5,6}). It joins the non-common parts of both sets.
Step 3
Exam Tip
\(A\setminus B={1,2}\) और \(B\setminus A={5,6}\), इसलिए संघ ({1,2,5,6}) है। यह दोनों में असमान भागों को जोड़ता है।
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यदि \(A={x:x\in \mathbb{N},x<8}\) और \(B={x:x\in \mathbb{N},x>4,x<10}\) हैं, तो \(A\setminus B\) क्या है?
If \(A={x:x\in \mathbb{N},x<8}\) and \(B={x:x\in \mathbb{N},x>4,x<10}\), what is \(A\setminus B\)?
#sets
#natural-numbers
#difference
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A ( {1,2,3,4} )
B ( {5,6,7} )
C ( {8,9} )
D ( {1,2,3,4,5,6,7,8,9} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,4} )
Step 1
Concept
\(A=\{1,2,3,4,5,6,7\}\) and \(B=\{5,6,7,8,9\}\), so \(A\setminus B={1,2,3,4}\). Read boundary signs carefully.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,4} ). \(A=\{1,2,3,4,5,6,7\}\) and \(B=\{5,6,7,8,9\}\), so \(A\setminus B={1,2,3,4}\). Read boundary signs carefully.
Step 3
Exam Tip
\(A=\{1,2,3,4,5,6,7\}\) और \(B=\{5,6,7,8,9\}\), इसलिए \(A\setminus B={1,2,3,4}\)। सीमा चिन्हों को ध्यान से पढ़ें।
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यदि \(A\cup B=A\) है, तो कौन सा संबंध सही है?
If \(A\cup B=A\), which relation is correct?
#sets
#reasoning
#subset-union
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A \(B\subseteq A\)
B \(A\subseteq B\)
C \(A\cap B=\emptyset\)
D \(A=\emptyset\)
Explanation opens after your attempt
Correct Answer
A. \(B\subseteq A\)
Step 1
Concept
If adding (B) does not change (A), then all elements of (B) are in (A). Hence \(B\subseteq A\).
Step 2
Why this answer is correct
The correct answer is A. \(B\subseteq A\). If adding (B) does not change (A), then all elements of (B) are in (A). Hence \(B\subseteq A\).
Step 3
Exam Tip
यदि (B) जोड़ने पर (A) नहीं बदलता, तो (B) के सभी अवयव (A) में हैं। इसलिए \(B\subseteq A\) है।
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यदि \(A\cap B=A\) है, तो कौन सा संबंध सही है?
If \(A\cap B=A\), which relation is correct?
#sets
#reasoning
#subset-intersection
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A \(A\subseteq B\)
B \(B\subseteq A\)
C \(A\cup B=A\)
D \(B=\emptyset\)
Explanation opens after your attempt
Correct Answer
A. \(A\subseteq B\)
Step 1
Concept
If the common part is the whole set (A), every element of (A) is also in (B). Hence \(A\subseteq B\).
Step 2
Why this answer is correct
The correct answer is A. \(A\subseteq B\). If the common part is the whole set (A), every element of (A) is also in (B). Hence \(A\subseteq B\).
Step 3
Exam Tip
यदि सामान्य भाग पूरा (A) है, तो (A) का हर अवयव (B) में भी है। इसलिए \(A\subseteq B\) है।
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यदि \(A=\{1,2,3,4,5,6\}\) और \(B=\{2,4,6\}\) हैं, तो \(A\setminus B\) तथा \(B\setminus A\) क्रमशः क्या हैं?
If \(A=\{1,2,3,4,5,6\}\) and \(B=\{2,4,6\}\), what are \(A\setminus B\) and \(B\setminus A\) respectively?
#sets
#difference
#subset
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A \( {1,3,5},\emptyset \)
B \( \emptyset,{1,3,5} \)
C ( {2,4,6},{1,3,5} )
D \( {1,2,3,4,5,6},\emptyset \)
Explanation opens after your attempt
Correct Answer
A. \( {1,3,5},\emptyset \)
Step 1
Concept
Since \(B\subseteq A\), \(A\setminus B={1,3,5}\) and \(B\setminus A=\emptyset\). In a subset case, smaller minus larger is empty.
Step 2
Why this answer is correct
The correct answer is A. \( {1,3,5},\emptyset \). Since \(B\subseteq A\), \(A\setminus B={1,3,5}\) and \(B\setminus A=\emptyset\). In a subset case, smaller minus larger is empty.
Step 3
Exam Tip
\(B\subseteq A\), इसलिए \(A\setminus B={1,3,5}\) और \(B\setminus A=\emptyset\)। उपसमुच्चय में छोटे से बड़े का अंतर रिक्त होता है।
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यदि \(A={x:x\in \mathbb{Z},x^2\le 4}\) और \(B=\{-1,0,1,3\}\) हैं, तो \(A\cap B\) क्या है?
If \(A={x:x\in \mathbb{Z},x^2\le 4}\) and \(B=\{-1,0,1,3\}\), what is \(A\cap B\)?
#sets
#integers
#intersection
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A ( {-2,-1,0,1,2} )
B ( {-1,0,1} )
C ( {3} )
D ( {-2,2,3} )
Explanation opens after your attempt
Correct Answer
B. ( {-1,0,1} )
Step 1
Concept
\(A=\{-2,-1,0,1,2\}\), so the common elements from (B) are (-1,0,1). In square conditions, also check negative integers.
Step 2
Why this answer is correct
The correct answer is B. ( {-1,0,1} ). \(A=\{-2,-1,0,1,2\}\), so the common elements from (B) are (-1,0,1). In square conditions, also check negative integers.
Step 3
Exam Tip
\(A=\{-2,-1,0,1,2\}\), इसलिए (B) से समान अवयव (-1,0,1) हैं। वर्ग वाली शर्त में ऋणात्मक पूर्णांक भी जांचें।
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यदि \(A=\{1,3,5,7,9\}\) और \(B=\{3,6,9\}\) हैं, तो कौन सा अवयव \(A\cup B\) में है लेकिन \(A\cap B\) में नहीं है?
If \(A=\{1,3,5,7,9\}\) and \(B=\{3,6,9\}\), which element is in \(A\cup B\) but not in \(A\cap B\)?
#sets
#reasoning
#union-minus-intersection
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A (3)
B (9)
C (5)
D (11)
Explanation opens after your attempt
Step 1
Concept
\(A\cap B={3,9}\), while (5) is in the union but not in the common part. In such questions, first remove common elements.
Step 2
Why this answer is correct
The correct answer is C. (5). \(A\cap B={3,9}\), while (5) is in the union but not in the common part. In such questions, first remove common elements.
Step 3
Exam Tip
\(A\cap B={3,9}\), जबकि (5) संघ में है पर सामान्य भाग में नहीं है। ऐसे प्रश्न में पहले सामान्य अवयव हटाएं।
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यदि \(A=\{2,4,6,8\}\) और \(B=\{1,2,3,4\}\) हैं, तो \(A\cap B\subseteq A\cup B\) के बारे में सही कथन कौन सा है?
If \(A=\{2,4,6,8\}\) and \(B=\{1,2,3,4\}\), which statement about \(A\cap B\subseteq A\cup B\) is correct?
#sets
#subset
#conceptual
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A यह हमेशा सत्य है / It is always true
B यह हमेशा असत्य है / It is always false
C यह तभी सत्य है जब (A=B) / It is true only when (A=B)
D यह तभी सत्य है जब \(A=\emptyset\) / It is true only when \(A=\emptyset\)
Explanation opens after your attempt
Correct Answer
A. यह हमेशा सत्य है / It is always true
Step 1
Concept
Every common element belongs to both sets, so it also belongs to the union. Hence \(A\cap B\subseteq A\cup B\) is always true.
Step 2
Why this answer is correct
The correct answer is A. यह हमेशा सत्य है / It is always true. Every common element belongs to both sets, so it also belongs to the union. Hence \(A\cap B\subseteq A\cup B\) is always true.
Step 3
Exam Tip
हर सामान्य अवयव दोनों समुच्चयों में होता है, इसलिए वह संघ में भी होता है। अतः \(A\cap B\subseteq A\cup B\) हमेशा सत्य है।
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यदि \(A=\{1,2,3,4\}\), \(B=\{2,4,6,8\}\) और \(C=\{4,8,12\}\) हैं, तो \(A\cap B\cap C\) क्या है?
If \(A=\{1,2,3,4\}\), \(B=\{2,4,6,8\}\), and \(C=\{4,8,12\}\), what is \(A\cap B\cap C\)?
#sets
#three-sets
#intersection
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A ( {2,4} )
B ( {4} )
C ( {8} )
D \( \emptyset \)
Explanation opens after your attempt
Correct Answer
B. ( {4} )
Step 1
Concept
Only (4) is common to all three sets. In intersection of three sets, the element must be in every set.
Step 2
Why this answer is correct
The correct answer is B. ( {4} ). Only (4) is common to all three sets. In intersection of three sets, the element must be in every set.
Step 3
Exam Tip
तीनों समुच्चयों में केवल (4) समान है। तीन समुच्चयों के प्रतिच्छेद में अवयव सभी में होना चाहिए।
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यदि \(A=\{m,n,o\}\) और \(B=\{n,o,p,q\}\) हैं, तो (\(A\cup B\)\setminus A) क्या है?
If \(A=\{m,n,o\}\) and \(B=\{n,o,p,q\}\), what is (\(A\cup B\)\setminus A)?
#sets
#identity
#difference
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A ( {p,q} )
B ( {m} )
C ( {n,o} )
D ( {m,n,o,p,q} )
Explanation opens after your attempt
Correct Answer
A. ( {p,q} )
Step 1
Concept
\(A\cup B={m,n,o,p,q}\), and removing (A) leaves (p,q). This equals \(B\setminus A\).
Step 2
Why this answer is correct
The correct answer is A. ( {p,q} ). \(A\cup B={m,n,o,p,q}\), and removing (A) leaves (p,q). This equals \(B\setminus A\).
Step 3
Exam Tip
\(A\cup B={m,n,o,p,q}\), इससे (A) हटाने पर (p,q) बचते हैं। यह \(B\setminus A\) के बराबर है।
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यदि \(A=\{1,2,3,4,5\}\) और \(B=\{4,5,6,7\}\) हैं, तो (\(A\cup B\)\setminus B) किसके बराबर है?
If \(A=\{1,2,3,4,5\}\) and \(B=\{4,5,6,7\}\), what is (\(A\cup B\)\setminus B) equal to?
#sets
#identity
#difference
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A ( {1,2,3} )
B ( {4,5} )
C ( {6,7} )
D ( {1,2,3,4,5,6,7} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3} )
Step 1
Concept
Removing all elements of (B) from the union leaves only the non-common elements of (A). So the answer is \(A\setminus B={1,2,3}\).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3} ). Removing all elements of (B) from the union leaves only the non-common elements of (A). So the answer is \(A\setminus B={1,2,3}\).
Step 3
Exam Tip
संघ से (B) के सभी अवयव हटाने पर केवल (A) के गैर-सामान्य अवयव बचते हैं। इसलिए उत्तर \(A\setminus B={1,2,3}\) है।
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यदि (n\(A\setminus B\)=9), (n\(A\cap B\)=6) और (n\(B\setminus A\)=11) हैं, तो (n\(A\cup B\)) कितना है?
If (n\(A\setminus B\)=9), (n\(A\cap B\)=6), and (n\(B\setminus A\)=11), what is (n\(A\cup B\))?
#sets
#venn-diagram
#cardinality
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A (15)
B (20)
C (26)
D (35)
Explanation opens after your attempt
Step 1
Concept
The union is made of three disjoint parts: \(A\setminus B\), \(A\cap B\), and \(B\setminus A\). Hence (9+6+11=26).
Step 2
Why this answer is correct
The correct answer is C. (26). The union is made of three disjoint parts: \(A\setminus B\), \(A\cap B\), and \(B\setminus A\). Hence (9+6+11=26).
Step 3
Exam Tip
संघ तीन अलग-अलग भागों \(A\setminus B\), \(A\cap B\), और \(B\setminus A\) से बनता है। इसलिए (9+6+11=26)।
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एक सर्वे में (45) लोग चाय पसंद करते हैं, (38) कॉफी पसंद करते हैं और (20) दोनों पसंद करते हैं। केवल चाय पसंद करने वालों की संख्या क्या है?
In a survey, (45) people like tea, (38) like coffee, and (20) like both. How many like only tea?
#sets
#word-problem
#difference
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A (25)
B (18)
C (63)
D (83)
Explanation opens after your attempt
Step 1
Concept
Only tea is (45-20=25). In only-type questions, subtract the common part.
Step 2
Why this answer is correct
The correct answer is A. (25). Only tea is (45-20=25). In only-type questions, subtract the common part.
Step 3
Exam Tip
केवल चाय (=45-20=25) है। केवल वाले प्रश्न में सामान्य भाग घटाएं।
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एक समूह में (32) विद्यार्थी क्रिकेट, (24) फुटबॉल और (12) दोनों खेलते हैं। केवल फुटबॉल खेलने वालों की संख्या क्या है?
In a group, (32) students play cricket, (24) play football, and (12) play both. How many play only football?
#sets
#word-problem
#only-set
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A (12)
B (20)
C (36)
D (44)
Explanation opens after your attempt
Step 1
Concept
Only football is (24-12=12). Those who play both are not included in only football.
Step 2
Why this answer is correct
The correct answer is A. (12). Only football is (24-12=12). Those who play both are not included in only football.
Step 3
Exam Tip
केवल फुटबॉल (=24-12=12) होगा। दोनों खेलने वालों को केवल फुटबॉल में शामिल नहीं किया जाता।
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यदि (n\(A\cup B\)=70), (n(A)=46) और (n\(B\setminus A\)=24) है, तो (n\(A\cap B\)) क्या है?
If (n\(A\cup B\)=70), (n(A)=46), and (n\(B\setminus A\)=24), what is (n\(A\cap B\))?
#sets
#cardinality
#tricky-question
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A (0)
B (22)
C (24)
D (46)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B\) is formed by (A) and \(B\setminus A\), giving (46+24=70). However (n\(A\cap B\)) is inside (A) and cannot be uniquely found from this data.
Step 2
Why this answer is correct
The correct answer is A. (0). \(A\cup B\) is formed by (A) and \(B\setminus A\), giving (46+24=70). However (n\(A\cap B\)) is inside (A) and cannot be uniquely found from this data.
Step 3
Exam Tip
\(A\cup B\) में (A) और \(B\setminus A\) मिलकर (46+24=70) हैं। इसलिए (B) का (A) से साझा भाग (A) के अंदर है, पर दिए गए डाटा से अतिरिक्त साझा भाग (0) नहीं बल्कि (n\(A\cap B\)) निश्चित नहीं होता।
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यदि (n(A)=46), (n(B)=35) और (n\(B\setminus A\)=24) है, तो (n\(A\cap B\)) कितना है?
If (n(A)=46), (n(B)=35), and (n\(B\setminus A\)=24), what is (n\(A\cap B\))?
#sets
#cardinality
#difference
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A (11)
B (22)
C (24)
D (35)
Explanation opens after your attempt
Step 1
Concept
(B) is divided into \(B\setminus A\) and \(A\cap B\). Therefore (n\(A\cap B\)=35-24=11).
Step 2
Why this answer is correct
The correct answer is A. (11). (B) is divided into \(B\setminus A\) and \(A\cap B\). Therefore (n\(A\cap B\)=35-24=11).
Step 3
Exam Tip
(B) दो भागों \(B\setminus A\) और \(A\cap B\) में बंटता है। इसलिए (n\(A\cap B\)=35-24=11)।
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यदि \(A=\{0,1,2,3\}\) और \(B=\{2,3,4,5\}\) हैं, तो \(A\cap B\) का उपसमुच्चय कौन सा है?
If \(A=\{0,1,2,3\}\) and \(B=\{2,3,4,5\}\), which is a subset of \(A\cap B\)?
#sets
#subset
#intersection
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A ( {2} )
B ( {4} )
C ( {0,1} )
D ( {2,4} )
Explanation opens after your attempt
Correct Answer
A. ( {2} )
Step 1
Concept
\(A\cap B={2,3}\), so ({2}) is its subset. In a subset, every element must belong to the original set.
Step 2
Why this answer is correct
The correct answer is A. ( {2} ). \(A\cap B={2,3}\), so ({2}) is its subset. In a subset, every element must belong to the original set.
Step 3
Exam Tip
\(A\cap B={2,3}\), इसलिए ({2}) इसका उपसमुच्चय है। उपसमुच्चय में हर अवयव मूल समुच्चय में होना चाहिए।
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यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{2,3,5,7\}\) और \(C=\{3,5,8\}\) हैं, तो (A\cap \(B\setminus C\)) क्या है?
If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,3,5,7\}\), and \(C=\{3,5,8\}\), what is (A\cap \(B\setminus C\))?
#sets
#mixed-operation
#difference-intersection
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A ( {2} )
B ( {3,5} )
C ( {7} )
D ( {2,7} )
Explanation opens after your attempt
Correct Answer
A. ( {2} )
Step 1
Concept
\(B\setminus C={2,7}\), then intersecting with (A) leaves (2). Do the difference first, then the intersection.
Step 2
Why this answer is correct
The correct answer is A. ( {2} ). \(B\setminus C={2,7}\), then intersecting with (A) leaves (2). Do the difference first, then the intersection.
Step 3
Exam Tip
\(B\setminus C={2,7}\), फिर (A) से प्रतिच्छेद लेने पर (2) बचता है। पहले अंतर और फिर प्रतिच्छेद करें।
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यदि \(A=\{a,b,c,e\}\), \(B=\{b,d,e\}\) और \(C=\{e,f\}\) हैं, तो (\(A\cup B\)\cap \(B\cup C\)) क्या है?
If \(A=\{a,b,c,e\}\), \(B=\{b,d,e\}\), and \(C=\{e,f\}\), what is (\(A\cup B\)\cap \(B\cup C\))?
#sets
#three-sets
#compound-operation
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A ( {b,d,e} )
B ( {a,c,f} )
C ( {e} )
D ( {a,b,c,d,e,f} )
Explanation opens after your attempt
Correct Answer
A. ( {b,d,e} )
Step 1
Concept
\(A\cup B={a,b,c,d,e}\) and \(B\cup C={b,d,e,f}\); their intersection is ({b,d,e}). Find both unions separately.
Step 2
Why this answer is correct
The correct answer is A. ( {b,d,e} ). \(A\cup B={a,b,c,d,e}\) and \(B\cup C={b,d,e,f}\); their intersection is ({b,d,e}). Find both unions separately.
Step 3
Exam Tip
\(A\cup B={a,b,c,d,e}\) और \(B\cup C={b,d,e,f}\), इनका प्रतिच्छेद ({b,d,e}) है। दोनों संघ अलग-अलग निकालें।
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यदि \(A=\{1,2,4,8\}\), \(B=\{2,4,6,8\}\) और \(C=\{4,8,10\}\) हैं, तो (\(A\cap B\)\setminus C) क्या है?
If \(A=\{1,2,4,8\}\), \(B=\{2,4,6,8\}\), and \(C=\{4,8,10\}\), what is (\(A\cap B\)\setminus C)?
#sets
#compound-operation
#difference
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A ( {2} )
B ( {4,8} )
C ( {1,6} )
D \( \emptyset \)
Explanation opens after your attempt
Correct Answer
A. ( {2} )
Step 1
Concept
\(A\cap B={2,4,8}\), and removing (4,8) from (C) leaves (2). Write every step in mixed questions.
Step 2
Why this answer is correct
The correct answer is A. ( {2} ). \(A\cap B={2,4,8}\), and removing (4,8) from (C) leaves (2). Write every step in mixed questions.
Step 3
Exam Tip
\(A\cap B={2,4,8}\), इसमें से (C) के (4,8) हटाने पर (2) बचता है। मिश्रित प्रश्न में हर चरण लिखें।
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यदि \(A={x:x\in \mathbb{N},1\le x\le 12}\), \(B=\{2,4,6,8,10,12\}\) और \(C=\{3,6,9,12\}\) हैं, तो (A\setminus \(B\cup C\)) क्या है?
If \(A={x:x\in \mathbb{N},1\le x\le 12}\), \(B=\{2,4,6,8,10,12\}\), and \(C=\{3,6,9,12\}\), what is (A\setminus \(B\cup C\))?
#sets
#universal-like-set
#difference
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A ( {1,5,7,11} )
B ( {2,3,4,6,8,9,10,12} )
C ( {6,12} )
D ( {1,2,3,4,5,6,7,8,9,10,11,12} )
Explanation opens after your attempt
Correct Answer
A. ( {1,5,7,11} )
Step 1
Concept
\(B\cup C={2,3,4,6,8,9,10,12}\); removing these from (A) leaves (1,5,7,11). First decide which elements must be removed.
Step 2
Why this answer is correct
The correct answer is A. ( {1,5,7,11} ). \(B\cup C={2,3,4,6,8,9,10,12}\); removing these from (A) leaves (1,5,7,11). First decide which elements must be removed.
Step 3
Exam Tip
\(B\cup C={2,3,4,6,8,9,10,12}\), इन्हें (A) से हटाने पर (1,5,7,11) बचते हैं। पहले हटाए जाने वाले अवयव तय करें।
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