यदि \(A=\{2,5,8,11\}\) और \(B=\{1,5,7,11,13\}\) हैं, तो \(A\cup B\) क्या है?
If \(A=\{2,5,8,11\}\) and \(B=\{1,5,7,11,13\}\), what is \(A\cup B\)?
#sets
#union
#finite-sets
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A ( {1,2,5,7,8,11,13} )
B ( {5,11} )
C ( {2,8} )
D ( {1,7,13} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,5,7,8,11,13} )
Step 1
Concept
\(A\cup B\) contains all distinct elements of both sets. Write repeated elements only once.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,5,7,8,11,13} ). \(A\cup B\) contains all distinct elements of both sets. Write repeated elements only once.
Step 3
Exam Tip
\(A\cup B\) में दोनों समुच्चयों के सभी अलग-अलग अवयव आते हैं। दोहराए गए अवयव केवल एक बार लिखें।
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यदि \(A={x:x\in\mathbb{N},x\mid 30}\) और \(B={x:x\in\mathbb{N},x\mid 45}\) हैं, तो (\(A\cup B\)\setminus\(A\cap B\)) क्या है?
If \(A={x:x\in\mathbb{N},x\mid 30}\) and \(B={x:x\in\mathbb{N},x\mid 45}\), what is (\(A\cup B\)\setminus\(A\cap B\))?
#sets
#factors
#symmetric-difference
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A ( {2,6,9,10,30,45} )
B ( {1,3,5,15} )
C ( {1,2,3,5,6,9,10,15,30,45} )
D \( \emptyset \)
Explanation opens after your attempt
Correct Answer
A. ( {2,6,9,10,30,45} )
Step 1
Concept
Here \(A\cap B={1,3,5,15}\), so the common part is removed from the union. In exams, first list all factors completely.
Step 2
Why this answer is correct
The correct answer is A. ( {2,6,9,10,30,45} ). Here \(A\cap B={1,3,5,15}\), so the common part is removed from the union. In exams, first list all factors completely.
Step 3
Exam Tip
यहां \(A\cap B={1,3,5,15}\) है, इसलिए संघ से सामान्य भाग हटता है। परीक्षा में पहले गुणनखंडों की पूरी सूची बनाएं।
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यदि \(A=\{4,6,8,10,12\}\) और \(B=\{3,6,9,12,15\}\) हैं, तो \(A\cap B\) ज्ञात कीजिए।
If \(A=\{4,6,8,10,12\}\) and \(B=\{3,6,9,12,15\}\), find \(A\cap B\).
#sets
#intersection
#common-elements
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A ( {6,12} )
B ( {4,8,10} )
C ( {3,9,15} )
D ( {3,4,6,8,9,10,12,15} )
Explanation opens after your attempt
Correct Answer
A. ( {6,12} )
Step 1
Concept
\(A\cap B\) contains only common elements. Here the common elements are (6) and (12).
Step 2
Why this answer is correct
The correct answer is A. ( {6,12} ). \(A\cap B\) contains only common elements. Here the common elements are (6) and (12).
Step 3
Exam Tip
\(A\cap B\) में केवल समान अवयव आते हैं। यहां समान अवयव (6) और (12) हैं।
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यदि \(A=\{1,2,3,4,5,6,7,8\}\), \(B=\{2,4,6,8,10\}\) और \(C=\{1,4,8,12\}\) हैं, तो (\(A\cap B\)\setminus C) क्या होगा?
If \(A=\{1,2,3,4,5,6,7,8\}\), \(B=\{2,4,6,8,10\}\), and \(C=\{1,4,8,12\}\), what is (\(A\cap B\)\setminus C)?
#sets
#compound-operation
#intersection-difference
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A ( {2,6} )
B ( {4,8} )
C ( {1,12} )
D ( {2,4,6,8} )
Explanation opens after your attempt
Correct Answer
A. ( {2,6} )
Step 1
Concept
First \(A\cap B={2,4,6,8}\). Removing (4) and (8) from (C) leaves ({2,6}).
Step 2
Why this answer is correct
The correct answer is A. ( {2,6} ). First \(A\cap B={2,4,6,8}\). Removing (4) and (8) from (C) leaves ({2,6}).
Step 3
Exam Tip
पहले \(A\cap B={2,4,6,8}\) मिलता है। इसमें से (C) के (4) और (8) हटाने पर ({2,6}) बचता है।
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यदि \(A=\{a,c,e,g,i\}\) और \(B=\{b,c,d,g,h\}\) हैं, तो \(A\setminus B\) क्या है?
If \(A=\{a,c,e,g,i\}\) and \(B=\{b,c,d,g,h\}\), what is \(A\setminus B\)?
#sets
#difference
#letters
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A ( {a,e,i} )
B ( {c,g} )
C ( {b,d,h} )
D ( {a,b,c,d,e,g,h,i} )
Explanation opens after your attempt
Correct Answer
A. ( {a,e,i} )
Step 1
Concept
\(A\setminus B\) keeps elements of (A) that are not in (B). So (c) and (g) are removed.
Step 2
Why this answer is correct
The correct answer is A. ( {a,e,i} ). \(A\setminus B\) keeps elements of (A) that are not in (B). So (c) and (g) are removed.
Step 3
Exam Tip
\(A\setminus B\) में (A) के वे अवयव रहते हैं जो (B) में नहीं हैं। इसलिए (c) और (g) हट जाते हैं।
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एक सर्वे में (58) विद्यार्थी ऑनलाइन कक्षा लेते हैं, (46) विद्यार्थी पुस्तकालय जाते हैं और (21) दोनों करते हैं। केवल एक ही गतिविधि करने वाले विद्यार्थियों की संख्या क्या है?
In a survey, (58) students take online classes, (46) students visit the library, and (21) do both. How many students do exactly one activity?
#sets
#word-problem
#exactly-one
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A (62)
B (83)
C (104)
D (37)
Explanation opens after your attempt
Step 1
Concept
Exactly one activity is ((58-21)+(46-21)=62). In such questions, subtract the both part from each group separately.
Step 2
Why this answer is correct
The correct answer is A. (62). Exactly one activity is ((58-21)+(46-21)=62). In such questions, subtract the both part from each group separately.
Step 3
Exam Tip
केवल एक गतिविधि (=(58-21)+(46-21)=62) है। ऐसे प्रश्न में दोनों वाले भाग को दोनों समूहों से अलग-अलग घटाएं।
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यदि \(A=\{1,4,9,16,25\}\) और \(B=\{4,16,36\}\) हैं, तो \(B\setminus A\) क्या होगा?
If \(A=\{1,4,9,16,25\}\) and \(B=\{4,16,36\}\), what is \(B\setminus A\)?
#sets
#difference
#order-sensitive
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A ( {36} )
B ( {4,16} )
C ( {1,9,25} )
D \( \emptyset \)
Explanation opens after your attempt
Correct Answer
A. ( {36} )
Step 1
Concept
In \(B\setminus A\), common elements of (A) are removed from (B). Removing (4) and (16) leaves (36).
Step 2
Why this answer is correct
The correct answer is A. ( {36} ). In \(B\setminus A\), common elements of (A) are removed from (B). Removing (4) and (16) leaves (36).
Step 3
Exam Tip
\(B\setminus A\) में (B) से (A) के सामान्य अवयव हटते हैं। (4) और (16) हटाने पर (36) बचता है।
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यदि \(A\setminus B=\emptyset\) और \(B\setminus A=\emptyset\) है, तो कौन सा निष्कर्ष सही है?
If \(A\setminus B=\emptyset\) and \(B\setminus A=\emptyset\), which conclusion is correct?
#sets
#reasoning
#equal-sets
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A (A=B)
B \(A\cap B=\emptyset\)
C \(A\cup B=\emptyset\)
D \(A\subset B\) हमेशा / \(A\subset B\) always
Explanation opens after your attempt
Step 1
Concept
Both differences being empty means neither set has any extra element. Therefore (A=B).
Step 2
Why this answer is correct
The correct answer is A. (A=B). Both differences being empty means neither set has any extra element. Therefore (A=B).
Step 3
Exam Tip
दोनों अंतरों के रिक्त होने का अर्थ है कि दोनों समुच्चयों में कोई अतिरिक्त अवयव नहीं है। इसलिए (A=B) होगा।
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\(यदि (A={x:x\in\mathbb{N},x\le 9,x\) विषम है\(}) और (B={x:x\in\mathbb{N},x<8,x\) अभाज्य है\(}) हैं, तो (A\cap B) क्या है\)?
\(If (A={x:x\in\mathbb{N},x\le 9,x\) is odd\(}) and (B={x:x\in\mathbb{N},x<8,x\) is prime\(}), what is (A\cap B)\)?
#sets
#set-builder
#intersection
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A ( {3,5,7} )
B ( {1,3,5,7,9} )
C ( {2,3,5,7} )
D ( {1,2,3,5,7,9} )
Explanation opens after your attempt
Correct Answer
A. ( {3,5,7} )
Step 1
Concept
\(A=\{1,3,5,7,9\}\) and \(B=\{2,3,5,7\}\), so the common elements are (3,5,7). Remember that (1) is not prime.
Step 2
Why this answer is correct
The correct answer is A. ( {3,5,7} ). \(A=\{1,3,5,7,9\}\) and \(B=\{2,3,5,7\}\), so the common elements are (3,5,7). Remember that (1) is not prime.
Step 3
Exam Tip
\(A=\{1,3,5,7,9\}\) और \(B=\{2,3,5,7\}\), इसलिए समान अवयव (3,5,7) हैं। (1) अभाज्य नहीं है।
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\(यदि (A={x:x\in\mathbb{Z},-5<x<4}) और (B={x:x\in\mathbb{Z},x\) सम है\(}) हैं, तथा केवल (B) के वे अवयव लिए जाएं जो (-5<x<4) को संतुष्ट करते हैं, तो (A\setminus B) क्या है\)?
\(If (A={x:x\in\mathbb{Z},-5<x<4}) and (B={x:x\in\mathbb{Z},x\) is even\(}), and only elements of (B) satisfying (-5<x<4) are considered, what is (A\setminus B)\)?
#sets
#integers
#difference
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A ( {-3,-1,1,3} )
B ( {-4,-2,0,2} )
C ( {-4,-3,-2,-1,0,1,2,3} )
D \( \emptyset \)
Explanation opens after your attempt
Correct Answer
A. ( {-3,-1,1,3} )
Step 1
Concept
\(A=\{-4,-3,-2,-1,0,1,2,3\}\), and the even elements are removed. Therefore the odd elements ({-3,-1,1,3}) remain.
Step 2
Why this answer is correct
The correct answer is A. ( {-3,-1,1,3} ). \(A=\{-4,-3,-2,-1,0,1,2,3\}\), and the even elements are removed. Therefore the odd elements ({-3,-1,1,3}) remain.
Step 3
Exam Tip
\(A=\{-4,-3,-2,-1,0,1,2,3\}\) है और सम अवयव हट जाते हैं। इसलिए विषम अवयव ({-3,-1,1,3}) बचते हैं।
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यदि \(A={x:x\in\mathbb{Z},-4\le x\le 1}\) और \(B={x:x\in\mathbb{Z},-1\le x\le 4}\) हैं, तो \(A\cup B\) क्या है?
If \(A={x:x\in\mathbb{Z},-4\le x\le 1}\) and \(B={x:x\in\mathbb{Z},-1\le x\le 4}\), what is \(A\cup B\)?
#sets
#integers
#union
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A ( {-4,-3,-2,-1,0,1,2,3,4} )
B ( {-1,0,1} )
C ( {-4,-3,-2} )
D ( {2,3,4} )
Explanation opens after your attempt
Correct Answer
A. ( {-4,-3,-2,-1,0,1,2,3,4} )
Step 1
Concept
Combining both integer intervals gives all integers from (-4) to (4). In union, write every available element.
Step 2
Why this answer is correct
The correct answer is A. ( {-4,-3,-2,-1,0,1,2,3,4} ). Combining both integer intervals gives all integers from (-4) to (4). In union, write every available element.
Step 3
Exam Tip
दोनों पूर्णांक अंतरालों को मिलाने पर (-4) से (4) तक सभी पूर्णांक मिलते हैं। संघ में सभी उपलब्ध अवयव लिखें।
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यदि \(A={x:x\in\mathbb{N},x^2\le 49}\) और \(B=\{2,4,6,8\}\) हैं, तो \(A\setminus B\) क्या है?
If \(A={x:x\in\mathbb{N},x^2\le 49}\) and \(B=\{2,4,6,8\}\), what is \(A\setminus B\)?
#sets
#inequality
#difference
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A ( {1,3,5,7} )
B ( {2,4,6} )
C ( {1,2,3,4,5,6,7} )
D ( {8} )
Explanation opens after your attempt
Correct Answer
A. ( {1,3,5,7} )
Step 1
Concept
\(A=\{1,2,3,4,5,6,7\}\), and (2,4,6) are removed from it. Hence \(A\setminus B={1,3,5,7}\).
Step 2
Why this answer is correct
The correct answer is A. ( {1,3,5,7} ). \(A=\{1,2,3,4,5,6,7\}\), and (2,4,6) are removed from it. Hence \(A\setminus B={1,3,5,7}\).
Step 3
Exam Tip
\(A=\{1,2,3,4,5,6,7\}\) है, इसमें से (2,4,6) हटते हैं। इसलिए \(A\setminus B={1,3,5,7}\)।
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यदि \(A=\{1,2,3,6\}\), \(B=\{2,3,5,6\}\) और \(C=\{3,6,9\}\) हैं, तो \(A\cap B\cap C\) क्या है?
If \(A=\{1,2,3,6\}\), \(B=\{2,3,5,6\}\), and \(C=\{3,6,9\}\), what is \(A\cap B\cap C\)?
#sets
#three-sets
#intersection
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A ( {3,6} )
B ( {2,3,6} )
C ( {1,5,9} )
D \( \emptyset \)
Explanation opens after your attempt
Correct Answer
A. ( {3,6} )
Step 1
Concept
Both (3) and (6) are in all three sets. In a three-set intersection, an element must be in every set.
Step 2
Why this answer is correct
The correct answer is A. ( {3,6} ). Both (3) and (6) are in all three sets. In a three-set intersection, an element must be in every set.
Step 3
Exam Tip
तीनों समुच्चयों में (3) और (6) दोनों हैं। तीन-समुच्चय प्रतिच्छेद में अवयव सभी समुच्चयों में होना चाहिए।
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यदि \(A=\{r,s,t,u\}\), \(B=\{s,u,v\}\) और \(C=\{u,v,w\}\) हैं, तो (A\cap\(B\cup C\)) क्या है?
If \(A=\{r,s,t,u\}\), \(B=\{s,u,v\}\), and \(C=\{u,v,w\}\), what is (A\cap\(B\cup C\))?
#sets
#mixed-operation
#union-intersection
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A ( {s,u} )
B ( {r,t} )
C ( {u,v} )
D ( {r,s,t,u,v,w} )
Explanation opens after your attempt
Correct Answer
A. ( {s,u} )
Step 1
Concept
First \(B\cup C={s,u,v,w}\). Its common part with (A) is ({s,u}).
Step 2
Why this answer is correct
The correct answer is A. ( {s,u} ). First \(B\cup C={s,u,v,w}\). Its common part with (A) is ({s,u}).
Step 3
Exam Tip
पहले \(B\cup C={s,u,v,w}\) है। इसका (A) से सामान्य भाग ({s,u}) है।
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यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{2,5,8\}\) और \(C=\{1,5,6,9\}\) हैं, तो (A\setminus\(B\cup C\)) क्या है?
If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,5,8\}\), and \(C=\{1,5,6,9\}\), what is (A\setminus\(B\cup C\))?
#sets
#difference
#compound-operation
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A ( {3,4} )
B ( {1,2,5,6} )
C ( {8,9} )
D ( {1,2,3,4,5,6,8,9} )
Explanation opens after your attempt
Correct Answer
A. ( {3,4} )
Step 1
Concept
\(B\cup C={1,2,5,6,8,9}\). Removing (1,2,5,6) from (A) leaves (3,4).
Step 2
Why this answer is correct
The correct answer is A. ( {3,4} ). \(B\cup C={1,2,5,6,8,9}\). Removing (1,2,5,6) from (A) leaves (3,4).
Step 3
Exam Tip
\(B\cup C={1,2,5,6,8,9}\) है। (A) से (1,2,5,6) हटाने पर (3,4) बचते हैं।
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यदि (n(A)=26), (n(B)=19) और (n\(A\cap B\)=8) है, तो (n\(A\cup B\)) क्या है?
If (n(A)=26), (n(B)=19), and (n\(A\cap B\)=8), what is (n\(A\cup B\))?
#sets
#cardinality
#union-formula
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A (37)
B (45)
C (53)
D (34)
Explanation opens after your attempt
Step 1
Concept
Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). Thus (26+19-8=37).
Step 2
Why this answer is correct
The correct answer is A. (37). Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). Thus (26+19-8=37).
Step 3
Exam Tip
सूत्र (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)) लगाएं। इसलिए (26+19-8=37)।
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यदि (n(A)=31), (n(B)=28) और (n\(A\cup B\)=46) है, तो (n\(A\cap B\)) कितना है?
If (n(A)=31), (n(B)=28), and (n\(A\cup B\)=46), what is (n\(A\cap B\))?
#sets
#cardinality
#intersection
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A (13)
B (15)
C (18)
D (21)
Explanation opens after your attempt
Step 1
Concept
By the formula, (n\(A\cap B\)=31+28-46=13). When union is given, find the common part using this formula.
Step 2
Why this answer is correct
The correct answer is A. (13). By the formula, (n\(A\cap B\)=31+28-46=13). When union is given, find the common part using this formula.
Step 3
Exam Tip
सूत्र से (n\(A\cap B\)=31+28-46=13) है। संघ दिया हो तो सामान्य भाग इसी सूत्र से निकालें।
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यदि (n\(A\setminus B\)=17) और (n\(A\cap B\)=11) है, तो (n(A)) क्या होगा?
If (n\(A\setminus B\)=17) and (n\(A\cap B\)=11), what is (n(A))?
#sets
#cardinality
#difference
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A (28)
B (17)
C (11)
D (6)
Explanation opens after your attempt
Step 1
Concept
Set (A) is made of two parts, \(A\setminus B\) and \(A\cap B\). Therefore (n(A)=17+11=28).
Step 2
Why this answer is correct
The correct answer is A. (28). Set (A) is made of two parts, \(A\setminus B\) and \(A\cap B\). Therefore (n(A)=17+11=28).
Step 3
Exam Tip
समुच्चय (A) दो भागों \(A\setminus B\) और \(A\cap B\) से बनता है। इसलिए (n(A)=17+11=28)।
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यदि (n(B)=42) और (n\(B\setminus A\)=25) है, तो (n\(A\cap B\)) क्या है?
If (n(B)=42) and (n\(B\setminus A\)=25), what is (n\(A\cap B\))?
#sets
#cardinality
#venn-parts
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A (17)
B (25)
C (42)
D (67)
Explanation opens after your attempt
Step 1
Concept
The two parts of (B) are \(B\setminus A\) and \(A\cap B\). Hence (n\(A\cap B\)=42-25=17).
Step 2
Why this answer is correct
The correct answer is A. (17). The two parts of (B) are \(B\setminus A\) and \(A\cap B\). Hence (n\(A\cap B\)=42-25=17).
Step 3
Exam Tip
(B) के दो भाग \(B\setminus A\) और \(A\cap B\) हैं। इसलिए (n\(A\cap B\)=42-25=17)।
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किसी विद्यालय में (36) विद्यार्थी संगीत, (29) चित्रकला और (14) दोनों सीखते हैं। कम से कम एक गतिविधि सीखने वाले विद्यार्थी कितने हैं?
In a school, (36) students learn music, (29) learn painting, and (14) learn both. How many students learn at least one activity?
#sets
#word-problem
#union
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A (51)
B (65)
C (43)
D (79)
Explanation opens after your attempt
Step 1
Concept
At least one means \(A\cup B\). Therefore (36+29-14=51).
Step 2
Why this answer is correct
The correct answer is A. (51). At least one means \(A\cup B\). Therefore (36+29-14=51).
Step 3
Exam Tip
कम से कम एक का अर्थ \(A\cup B\) है। इसलिए (36+29-14=51)।
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एक कक्षा में (40) विद्यार्थी गणित, (34) विज्ञान और (18) दोनों पढ़ते हैं। केवल गणित पढ़ने वाले विद्यार्थी कितने हैं?
In a class, (40) students study mathematics, (34) study science, and (18) study both. How many study only mathematics?
#sets
#word-problem
#only-one
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A (22)
B (16)
C (56)
D (74)
Explanation opens after your attempt
Step 1
Concept
Only mathematics is (40-18=22). In only-type questions, subtract the both part.
Step 2
Why this answer is correct
The correct answer is A. (22). Only mathematics is (40-18=22). In only-type questions, subtract the both part.
Step 3
Exam Tip
केवल गणित (=40-18=22) है। केवल वाले प्रश्न में दोनों वाले भाग को घटाएं।
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एक सर्वे में (52) लोग बस, (47) मेट्रो और (23) दोनों से यात्रा करते हैं। केवल मेट्रो से यात्रा करने वालों की संख्या क्या है?
In a survey, (52) people travel by bus, (47) by metro, and (23) by both. How many travel only by metro?
#sets
#word-problem
#difference
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A (24)
B (29)
C (76)
D (99)
Explanation opens after your attempt
Step 1
Concept
Only metro is (47-23=24). Do not count those using both in only metro.
Step 2
Why this answer is correct
The correct answer is A. (24). Only metro is (47-23=24). Do not count those using both in only metro.
Step 3
Exam Tip
केवल मेट्रो (=47-23=24) है। दोनों में आने वालों को केवल मेट्रो में न गिनें।
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यदि (n\(A\setminus B\)=12), (n\(A\cap B\)=7) और (n\(B\setminus A\)=16) हैं, तो (n\(A\cup B\)) क्या है?
If (n\(A\setminus B\)=12), (n\(A\cap B\)=7), and (n\(B\setminus A\)=16), what is (n\(A\cup B\))?
#sets
#venn-diagram
#cardinality
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A (35)
B (28)
C (19)
D (42)
Explanation opens after your attempt
Step 1
Concept
The union is the sum of three disjoint parts. Therefore (n\(A\cup B\)=12+7+16=35).
Step 2
Why this answer is correct
The correct answer is A. (35). The union is the sum of three disjoint parts. Therefore (n\(A\cup B\)=12+7+16=35).
Step 3
Exam Tip
संघ तीन अलग-अलग भागों का योग है। इसलिए (n\(A\cup B\)=12+7+16=35)।
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यदि \(A\subseteq B\) है, तो (\(A\cup B\)\cap A) किसके बराबर होगा?
If \(A\subseteq B\), what is (\(A\cup B\)\cap A) equal to?
#sets
#subset
#mixed-law
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A (A)
B (B)
C \(A\setminus B\)
D \( \emptyset \)
Explanation opens after your attempt
Step 1
Concept
When \(A\subseteq B\), \(A\cup B=B\) and \(B\cap A=A\). In subset questions, identify the larger and smaller sets.
Step 2
Why this answer is correct
The correct answer is A. (A). When \(A\subseteq B\), \(A\cup B=B\) and \(B\cap A=A\). In subset questions, identify the larger and smaller sets.
Step 3
Exam Tip
जब \(A\subseteq B\), तब \(A\cup B=B\) और \(B\cap A=A\) होता है। उपसमुच्चय प्रश्न में बड़ा और छोटा समुच्चय पहचानें।
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यदि \(B\subseteq A\) है, तो \(B\setminus A\) क्या होगा?
If \(B\subseteq A\), what is \(B\setminus A\)?
#sets
#subset
#difference
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A \( \emptyset \)
B (A)
C (B)
D \(A\cup B\)
Explanation opens after your attempt
Correct Answer
A. \( \emptyset \)
Step 1
Concept
If every element of (B) is in (A), nothing remains in (B) that is not in (A). Hence \(B\setminus A=\emptyset\).
Step 2
Why this answer is correct
The correct answer is A. \( \emptyset \). If every element of (B) is in (A), nothing remains in (B) that is not in (A). Hence \(B\setminus A=\emptyset\).
Step 3
Exam Tip
यदि (B) का हर अवयव (A) में है, तो (B) में ऐसा कुछ नहीं बचता जो (A) में न हो। इसलिए \(B\setminus A=\emptyset\)।
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यदि \(A\cap B=\emptyset\), (n(A)=15) और (n(B)=18) है, तो (n\(A\cup B\)) क्या है?
If \(A\cap B=\emptyset\), (n(A)=15), and (n(B)=18), what is (n\(A\cup B\))?
#sets
#disjoint
#cardinality
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A (33)
B (18)
C (15)
D (3)
Explanation opens after your attempt
Step 1
Concept
For disjoint sets, the common part is (0). Therefore (n\(A\cup B\)=15+18=33).
Step 2
Why this answer is correct
The correct answer is A. (33). For disjoint sets, the common part is (0). Therefore (n\(A\cup B\)=15+18=33).
Step 3
Exam Tip
असंबद्ध समुच्चयों में सामान्य भाग (0) होता है। इसलिए (n\(A\cup B\)=15+18=33)।
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यदि \(A=\{2,4,6\}\) और \(B=\{1,3,5,7\}\) हैं, तो कौन सा कथन सही है?
If \(A=\{2,4,6\}\) and \(B=\{1,3,5,7\}\), which statement is correct?
#sets
#disjoint
#conceptual
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A \(A\cap B=\emptyset\)
B \(A\cup B=\emptyset\)
C \(A\setminus B=\emptyset\)
D \(B\setminus A=\emptyset\)
Explanation opens after your attempt
Correct Answer
A. \(A\cap B=\emptyset\)
Step 1
Concept
(A) has even numbers and (B) has odd numbers, so there is no common element. Hence the intersection is empty.
Step 2
Why this answer is correct
The correct answer is A. \(A\cap B=\emptyset\). (A) has even numbers and (B) has odd numbers, so there is no common element. Hence the intersection is empty.
Step 3
Exam Tip
(A) में सम संख्याएं और (B) में विषम संख्याएं हैं, इसलिए कोई समान अवयव नहीं है। अतः प्रतिच्छेद रिक्त है।
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कौन सा नियम (A\cup\(B\cap C\)=\(A\cup B\)\cap\(A\cup C\)) को दर्शाता है?
Which law is represented by (A\cup\(B\cap C\)=\(A\cup B\)\cap\(A\cup C\))?
#sets
#laws
#distributive-law
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A वितरण नियम / Distributive law
B क्रमविनिमेय नियम / Commutative law
C साहचर्य नियम / Associative law
D निष्प्रभावी नियम / Idempotent law
Explanation opens after your attempt
Correct Answer
A. वितरण नियम / Distributive law
Step 1
Concept
This is distribution of union over intersection. In the distributive law, the outside set combines with both parts.
Step 2
Why this answer is correct
The correct answer is A. वितरण नियम / Distributive law. This is distribution of union over intersection. In the distributive law, the outside set combines with both parts.
Step 3
Exam Tip
यह संघ का प्रतिच्छेद पर वितरण है। वितरण नियम में बाहर का समुच्चय दोनों भागों के साथ जुड़ता है।
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यदि \(A\cap B=B\) है, तो कौन सा संबंध सही है?
If \(A\cap B=B\), which relation is correct?
#sets
#reasoning
#intersection-subset
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A \(B\subseteq A\)
B \(A\subseteq B\)
C \(A\cup B=B\)
D \(A\setminus B=\emptyset\)
Explanation opens after your attempt
Correct Answer
A. \(B\subseteq A\)
Step 1
Concept
When the common part is the whole set (B), every element of (B) is in (A). Thus \(B\subseteq A\).
Step 2
Why this answer is correct
The correct answer is A. \(B\subseteq A\). When the common part is the whole set (B), every element of (B) is in (A). Thus \(B\subseteq A\).
Step 3
Exam Tip
जब सामान्य भाग पूरा (B) है, तो (B) का हर अवयव (A) में है। अतः \(B\subseteq A\)।
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यदि \(A=\{1,3,5,7\}\) और \(B=\{3,7,9\}\) हैं, तो (\(A\cup B\)\setminus\(A\cap B\)) क्या है?
If \(A=\{1,3,5,7\}\) and \(B=\{3,7,9\}\), what is (\(A\cup B\)\setminus\(A\cap B\))?
#sets
#symmetric-difference
#compound
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A ( {1,5,9} )
B ( {3,7} )
C ( {1,3,5,7,9} )
D \( \emptyset \)
Explanation opens after your attempt
Correct Answer
A. ( {1,5,9} )
Step 1
Concept
The union is ( {1,3,5,7,9} ) and the intersection is ( {3,7} ). Removing the intersection leaves ( {1,5,9} ).
Step 2
Why this answer is correct
The correct answer is A. ( {1,5,9} ). The union is ( {1,3,5,7,9} ) and the intersection is ( {3,7} ). Removing the intersection leaves ( {1,5,9} ).
Step 3
Exam Tip
संघ ( {1,3,5,7,9} ) और प्रतिच्छेद ( {3,7} ) है। प्रतिच्छेद हटाने पर ( {1,5,9} ) बचता है।
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यदि \(A=\{2,3,5,7,11\}\) और \(B=\{1,3,5,9,11\}\) हैं, तो (\(A\setminus B\)\cup\(B\setminus A\)) क्या है?
If \(A=\{2,3,5,7,11\}\) and \(B=\{1,3,5,9,11\}\), what is (\(A\setminus B\)\cup\(B\setminus A\))?
#sets
#difference
#symmetric-difference
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A ( {1,2,7,9} )
B ( {3,5,11} )
C ( {1,2,3,5,7,9,11} )
D \( \emptyset \)
Explanation opens after your attempt
Correct Answer
A. ( {1,2,7,9} )
Step 1
Concept
\(A\setminus B={2,7}\) and \(B\setminus A={1,9}\). Their union is ({1,2,7,9}).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,7,9} ). \(A\setminus B={2,7}\) and \(B\setminus A={1,9}\). Their union is ({1,2,7,9}).
Step 3
Exam Tip
\(A\setminus B={2,7}\) और \(B\setminus A={1,9}\) है। दोनों का संघ ({1,2,7,9}) है।
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यदि \(A=\{2,4,6,8,10\}\), \(B=\{4,8,12\}\) और \(C=\{2,8,14\}\) हैं, तो (\(A\cap B\)\cup C) क्या है?
If \(A=\{2,4,6,8,10\}\), \(B=\{4,8,12\}\), and \(C=\{2,8,14\}\), what is (\(A\cap B\)\cup C)?
#sets
#mixed-operation
#three-sets
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A ( {2,4,8,14} )
B ( {4,8} )
C ( {2,8,14} )
D ( {2,4,6,8,10,12,14} )
Explanation opens after your attempt
Correct Answer
A. ( {2,4,8,14} )
Step 1
Concept
\(A\cap B={4,8}\). Taking union with (C) gives ({2,4,8,14}).
Step 2
Why this answer is correct
The correct answer is A. ( {2,4,8,14} ). \(A\cap B={4,8}\). Taking union with (C) gives ({2,4,8,14}).
Step 3
Exam Tip
\(A\cap B={4,8}\) है। (C) से संघ लेने पर ({2,4,8,14}) मिलता है।
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यदि \(A=\{1,2,4,6,8\}\), \(B=\{2,3,6,9\}\) और \(C=\{6,8,10\}\) हैं, तो (\(A\cup B\)\cap C) क्या है?
If \(A=\{1,2,4,6,8\}\), \(B=\{2,3,6,9\}\), and \(C=\{6,8,10\}\), what is (\(A\cup B\)\cap C)?
#sets
#mixed-operation
#union-intersection
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A ( {6,8} )
B ( {2,6} )
C ( {10} )
D ( {1,2,3,4,6,8,9,10} )
Explanation opens after your attempt
Correct Answer
A. ( {6,8} )
Step 1
Concept
\(A\cup B={1,2,3,4,6,8,9}\). Its intersection with (C) is ({6,8}).
Step 2
Why this answer is correct
The correct answer is A. ( {6,8} ). \(A\cup B={1,2,3,4,6,8,9}\). Its intersection with (C) is ({6,8}).
Step 3
Exam Tip
\(A\cup B={1,2,3,4,6,8,9}\) है। इसका (C) से प्रतिच्छेद ({6,8}) है।
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\(यदि (A={x:x\in\mathbb{N},x\) is a factor of \(24}) और (B={x:x\in\mathbb{N},x\) is a factor of \(36}) हैं, तो (A\cap B) क्या है\)?
\(If (A={x:x\in\mathbb{N},x\) is a factor of \(24}) and (B={x:x\in\mathbb{N},x\) is a factor of \(36}), what is (A\cap B)\)?
#sets
#factors
#intersection
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A ( {1,2,3,4,6,12} )
B ( {8,24} )
C ( {9,18,36} )
D ( {1,2,3,4,6,8,9,12,18,24,36} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,4,6,12} )
Step 1
Concept
The common factors of (24) and (36) are (1,2,3,4,6,12). In factor questions, first make both lists.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,4,6,12} ). The common factors of (24) and (36) are (1,2,3,4,6,12). In factor questions, first make both lists.
Step 3
Exam Tip
(24) और (36) के सामान्य गुणनखंड (1,2,3,4,6,12) हैं। गुणनखंड वाले प्रश्न में पहले दोनों सूचियां बनाएं।
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यदि \(A={x:x\in\mathbb{N},3\mid x,x\le 21}\) और \(B={x:x\in\mathbb{N},7\mid x,x\le 21}\) हैं, तो \(A\cup B\) क्या है?
If \(A={x:x\in\mathbb{N},3\mid x,x\le 21}\) and \(B={x:x\in\mathbb{N},7\mid x,x\le 21}\), what is \(A\cup B\)?
#sets
#multiples
#union
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A ( {3,6,7,9,12,14,15,18,21} )
B ( {21} )
C ( {3,6,9,12,15,18,21} )
D ( {7,14,21} )
Explanation opens after your attempt
Correct Answer
A. ( {3,6,7,9,12,14,15,18,21} )
Step 1
Concept
(A) has multiples of (3), and (B) has multiples of (7). In the union, do not write (21) twice.
Step 2
Why this answer is correct
The correct answer is A. ( {3,6,7,9,12,14,15,18,21} ). (A) has multiples of (3), and (B) has multiples of (7). In the union, do not write (21) twice.
Step 3
Exam Tip
(A) में (3) के गुणज और (B) में (7) के गुणज हैं। संघ में (21) को दो बार नहीं लिखते।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,5,10\}\) और \(B=\{2,4,6,8,10\}\) हैं, तो \(A\cup B\) क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,5,10\}\), and \(B=\{2,4,6,8,10\}\), what is \(A\cup B\)?
#sets
#universal-set
#union
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A ( {1,2,4,5,6,8,10} )
B ( {2,10} )
C ( {3,7,9} )
D ( {1,2,3,4,5,6,7,8,9,10} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,4,5,6,8,10} )
Step 1
Concept
The union contains all distinct elements of (A) and (B). (U) only gives the universal boundary.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,4,5,6,8,10} ). The union contains all distinct elements of (A) and (B). (U) only gives the universal boundary.
Step 3
Exam Tip
संघ में (A) और (B) के सभी अलग-अलग अवयव आते हैं। (U) केवल सार्वत्रिक सीमा देता है।
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यदि \(U=\{a,b,c,d,e,f,g\}\), \(A=\{a,c,e,g\}\) और \(B=\{b,c,e,f\}\) हैं, तो \(A\cap B\) क्या है?
If \(U=\{a,b,c,d,e,f,g\}\), \(A=\{a,c,e,g\}\), and \(B=\{b,c,e,f\}\), what is \(A\cap B\)?
#sets
#universal-set
#intersection
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A ( {c,e} )
B ( {a,g} )
C ( {b,f} )
D ( {d} )
Explanation opens after your attempt
Correct Answer
A. ( {c,e} )
Step 1
Concept
Both (A) and (B) contain (c) and (e). Keep only shared elements in the intersection.
Step 2
Why this answer is correct
The correct answer is A. ( {c,e} ). Both (A) and (B) contain (c) and (e). Keep only shared elements in the intersection.
Step 3
Exam Tip
(A) और (B) दोनों में (c) और (e) हैं। प्रतिच्छेद में केवल साझा अवयव रखें।
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यदि \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6\}\) हैं, तो (A\cap\(B\setminus A\)) क्या है?
If \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), what is (A\cap\(B\setminus A\))?
#sets
#identity
#difference-intersection
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A \( \emptyset \)
B ( {3,4} )
C ( {5,6} )
D ( {1,2,5,6} )
Explanation opens after your attempt
Correct Answer
A. \( \emptyset \)
Step 1
Concept
\(B\setminus A={5,6}\), and it has no element of (A). Hence the intersection is empty.
Step 2
Why this answer is correct
The correct answer is A. \( \emptyset \). \(B\setminus A={5,6}\), and it has no element of (A). Hence the intersection is empty.
Step 3
Exam Tip
\(B\setminus A={5,6}\) है और इसमें (A) का कोई अवयव नहीं है। इसलिए प्रतिच्छेद रिक्त है।
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यदि \(A=\{m,n,p,q\}\) और \(B=\{n,q,r,s\}\) हैं, तो (A\cup\(B\setminus A\)) क्या है?
If \(A=\{m,n,p,q\}\) and \(B=\{n,q,r,s\}\), what is (A\cup\(B\setminus A\))?
#sets
#identity
#union-difference
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A ( {m,n,p,q,r,s} )
B ( {r,s} )
C ( {n,q} )
D ( {m,p} )
Explanation opens after your attempt
Correct Answer
A. ( {m,n,p,q,r,s} )
Step 1
Concept
\(B\setminus A={r,s}\). Combining it with (A) gives the complete set same as \(A\cup B\).
Step 2
Why this answer is correct
The correct answer is A. ( {m,n,p,q,r,s} ). \(B\setminus A={r,s}\). Combining it with (A) gives the complete set same as \(A\cup B\).
Step 3
Exam Tip
\(B\setminus A={r,s}\) है। इसे (A) से मिलाने पर \(A\cup B\) जैसा पूरा समुच्चय मिलता है।
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यदि \(A=\{1,2,3,4,5\}\) और \(B=\{2,4\}\) हैं, तो (\(A\setminus B\)\cup B) क्या है?
If \(A=\{1,2,3,4,5\}\) and \(B=\{2,4\}\), what is (\(A\setminus B\)\cup B)?
#sets
#subset
#identity
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A ( {1,2,3,4,5} )
B ( {1,3,5} )
C ( {2,4} )
D \( \emptyset \)
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,4,5} )
Step 1
Concept
Since \(B\subseteq A\), \(A\setminus B={1,3,5}\). Union with (B) gives the whole set (A) back.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,4,5} ). Since \(B\subseteq A\), \(A\setminus B={1,3,5}\). Union with (B) gives the whole set (A) back.
Step 3
Exam Tip
क्योंकि \(B\subseteq A\), \(A\setminus B={1,3,5}\) है। इसे (B) से मिलाने पर पूरा (A) वापस मिलता है।
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यदि \(A=\{2,3,4,5,6\}\) और \(B=\{4,6,8\}\) हैं, तो \(A\cup B\) में है लेकिन \(A\cap B\) में नहीं है, ऐसा अवयव कौन सा है?
If \(A=\{2,3,4,5,6\}\) and \(B=\{4,6,8\}\), which element is in \(A\cup B\) but not in \(A\cap B\)?
#sets
#reasoning
#union-minus-intersection
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A (5)
B (4)
C (6)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(A\cap B={4,6}\), while (5) is in the union but not in the intersection. Identify common elements first.
Step 2
Why this answer is correct
The correct answer is A. (5). \(A\cap B={4,6}\), while (5) is in the union but not in the intersection. Identify common elements first.
Step 3
Exam Tip
\(A\cap B={4,6}\) है, जबकि (5) संघ में है पर प्रतिच्छेद में नहीं। पहले साझा अवयव पहचानें।
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यदि \(A=\{1,3,6,9\}\) और \(B=\{3,6,12\}\) हैं, तो कौन सा अवयव \(A\setminus B\) में है?
If \(A=\{1,3,6,9\}\) and \(B=\{3,6,12\}\), which element belongs to \(A\setminus B\)?
#sets
#membership
#difference
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A (9)
B (3)
C (6)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(A\setminus B={1,9}\). Among the options, only (9) belongs to this difference.
Step 2
Why this answer is correct
The correct answer is A. (9). \(A\setminus B={1,9}\). Among the options, only (9) belongs to this difference.
Step 3
Exam Tip
\(A\setminus B={1,9}\) है। विकल्पों में केवल (9) इस अंतर में आता है।
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यदि \(A=\{2,5,10\}\) और \(B=\{5,10,15\}\) हैं, तो कौन सा समुच्चय \(A\cap B\) का उपसमुच्चय है?
If \(A=\{2,5,10\}\) and \(B=\{5,10,15\}\), which set is a subset of \(A\cap B\)?
#sets
#subset
#intersection
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A ( {5} )
B ( {2} )
C ( {15} )
D ( {2,15} )
Explanation opens after your attempt
Correct Answer
A. ( {5} )
Step 1
Concept
\(A\cap B={5,10}\). Every element of ({5}) is in it, so it is a subset.
Step 2
Why this answer is correct
The correct answer is A. ( {5} ). \(A\cap B={5,10}\). Every element of ({5}) is in it, so it is a subset.
Step 3
Exam Tip
\(A\cap B={5,10}\) है। ({5}) का हर अवयव इसमें है, इसलिए यह उपसमुच्चय है।
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यदि \(A=\{0,2,4,6\}\) और \(B=\{1,2,3,4\}\) हैं, तो कौन सा कथन असत्य है?
If \(A=\{0,2,4,6\}\) and \(B=\{1,2,3,4\}\), which statement is false?
#sets
#false-statement
#union
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A \(A\cap B={2,4}\)
B \(A\setminus B={0,6}\)
C \(B\setminus A={1,3}\)
D \(A\cup B={2,4}\)
Explanation opens after your attempt
Correct Answer
D. \(A\cup B={2,4}\)
Step 1
Concept
\(A\cup B\) should be the set of all distinct elements, not only the common part. The correct union is ({0,1,2,3,4,6}).
Step 2
Why this answer is correct
The correct answer is D. \(A\cup B={2,4}\). \(A\cup B\) should be the set of all distinct elements, not only the common part. The correct union is ({0,1,2,3,4,6}).
Step 3
Exam Tip
\(A\cup B\) सभी अलग-अलग अवयवों का समुच्चय होना चाहिए, केवल सामान्य भाग नहीं। सही संघ ({0,1,2,3,4,6}) है।
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\(यदि (A={x:x\in\mathbb{N},x\le 15,x\) is composite\(}) और (B={4,6,8,10,12,14}) हैं, तो (B\setminus A) क्या है\)?
\(If (A={x:x\in\mathbb{N},x\le 15,x\) is composite\(}) and (B={4,6,8,10,12,14}), what is (B\setminus A)\)?
#sets
#composite-numbers
#difference
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A \( \emptyset \)
B ( {4,6,8} )
C ( {10,12,14} )
D ( {1,2,3,5,7,11,13} )
Explanation opens after your attempt
Correct Answer
A. \( \emptyset \)
Step 1
Concept
All elements of (B) are composite numbers up to (15), so \(B\subseteq A\). Hence \(B\setminus A=\emptyset\).
Step 2
Why this answer is correct
The correct answer is A. \( \emptyset \). All elements of (B) are composite numbers up to (15), so \(B\subseteq A\). Hence \(B\setminus A=\emptyset\).
Step 3
Exam Tip
(B) के सभी अवयव (15) तक की संयुक्त संख्याएं हैं, इसलिए \(B\subseteq A\)। अतः \(B\setminus A=\emptyset\)।
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यदि \(A=\{1,2,3,4,5,6,7,8\}\), \(B=\{2,4,6,8\}\) और \(C=\{1,2,3,4\}\) हैं, तो \(B\setminus C\) क्या है?
If \(A=\{1,2,3,4,5,6,7,8\}\), \(B=\{2,4,6,8\}\), and \(C=\{1,2,3,4\}\), what is \(B\setminus C\)?
#sets
#difference
#finite-sets
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A ( {6,8} )
B ( {2,4} )
C ( {1,3} )
D ( {5,7} )
Explanation opens after your attempt
Correct Answer
A. ( {6,8} )
Step 1
Concept
The common elements (2) and (4) of (C) are removed from (B). Hence \(B\setminus C={6,8}\).
Step 2
Why this answer is correct
The correct answer is A. ( {6,8} ). The common elements (2) and (4) of (C) are removed from (B). Hence \(B\setminus C={6,8}\).
Step 3
Exam Tip
(B) से (C) के सामान्य अवयव (2) और (4) हटते हैं। इसलिए \(B\setminus C={6,8}\)।
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यदि \(A=\{1,4,7,10\}\), \(B=\{2,4,8,10\}\) और \(C=\{4,10,12\}\) हैं, तो (\(A\cup B\)\cap C) क्या है?
If \(A=\{1,4,7,10\}\), \(B=\{2,4,8,10\}\), and \(C=\{4,10,12\}\), what is (\(A\cup B\)\cap C)?
#sets
#compound-operation
#intersection
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A ( {4,10} )
B ( {12} )
C ( {1,2,7,8} )
D ( {1,2,4,7,8,10,12} )
Explanation opens after your attempt
Correct Answer
A. ( {4,10} )
Step 1
Concept
\(A\cup B={1,2,4,7,8,10}\). Its common part with (C) is (4,10).
Step 2
Why this answer is correct
The correct answer is A. ( {4,10} ). \(A\cup B={1,2,4,7,8,10}\). Its common part with (C) is (4,10).
Step 3
Exam Tip
\(A\cup B={1,2,4,7,8,10}\) है। इसका (C) से सामान्य भाग (4,10) है।
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यदि \(A=\{p,q,r,s,t\}\), \(B=\{q,s,u\}\) और \(C=\{r,s,t,u\}\) हैं, तो (A\setminus\(B\cap C\)) क्या है?
If \(A=\{p,q,r,s,t\}\), \(B=\{q,s,u\}\), and \(C=\{r,s,t,u\}\), what is (A\setminus\(B\cap C\))?
#sets
#compound-operation
#difference
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A ( {p,q,r,t} )
B ( {s,u} )
C ( {s} )
D ( {p} )
Explanation opens after your attempt
Correct Answer
A. ( {p,q,r,t} )
Step 1
Concept
\(B\cap C={s,u}\), but only (s) is removed from (A). Thus (A\setminus\(B\cap C\)={p,q,r,t}).
Step 2
Why this answer is correct
The correct answer is A. ( {p,q,r,t} ). \(B\cap C={s,u}\), but only (s) is removed from (A). Thus (A\setminus\(B\cap C\)={p,q,r,t}).
Step 3
Exam Tip
\(B\cap C={s,u}\), लेकिन (A) में केवल (s) हटेगा। इसलिए (A\setminus\(B\cap C\)={p,q,r,t})।
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यदि \(A=\{1,2,3,4\}\) और \(B=\{2,4,6,8\}\) हैं, तो \(A\setminus B\subseteq A\) के बारे में सही कथन कौन सा है?
If \(A=\{1,2,3,4\}\) and \(B=\{2,4,6,8\}\), which statement about \(A\setminus B\subseteq A\) is correct?
#sets
#subset
#difference-property
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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 \(B=\emptyset\) / It is true only when \(B=\emptyset\)
Explanation opens after your attempt
Correct Answer
A. यह हमेशा सत्य है / It is always true
Step 1
Concept
\(A\setminus B\) contains only some elements of (A). Therefore \(A\setminus B\subseteq A\) is always true.
Step 2
Why this answer is correct
The correct answer is A. यह हमेशा सत्य है / It is always true. \(A\setminus B\) contains only some elements of (A). Therefore \(A\setminus B\subseteq A\) is always true.
Step 3
Exam Tip
\(A\setminus B\) में केवल (A) के ही कुछ अवयव बचते हैं। इसलिए \(A\setminus B\subseteq A\) हमेशा सत्य है।
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यदि \(A={x:x\in\mathbb{N},1\le x\le 10}\), \(B=\{1,4,7,10\}\) और \(C=\{2,4,6,8,10\}\) हैं, तो (A\setminus\(B\cup C\)) क्या है?
If \(A={x:x\in\mathbb{N},1\le x\le 10}\), \(B=\{1,4,7,10\}\), and \(C=\{2,4,6,8,10\}\), what is (A\setminus\(B\cup C\))?
#sets
#natural-numbers
#difference
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A ( {3,5,9} )
B ( {1,2,4,6,7,8,10} )
C ( {4,10} )
D ( {1,2,3,4,5,6,7,8,9,10} )
Explanation opens after your attempt
Correct Answer
A. ( {3,5,9} )
Step 1
Concept
\(B\cup C={1,2,4,6,7,8,10}\). Removing these from (A) leaves ({3,5,9}).
Step 2
Why this answer is correct
The correct answer is A. ( {3,5,9} ). \(B\cup C={1,2,4,6,7,8,10}\). Removing these from (A) leaves ({3,5,9}).
Step 3
Exam Tip
\(B\cup C={1,2,4,6,7,8,10}\) है। इन्हें (A) से हटाने पर ({3,5,9}) बचता है।
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