यदि \(A=\{2,4,6,8\}\) और \(B=\{6,8,10,12\}\) है, तो \(A\cup B\) क्या है?
If \(A=\{2,4,6,8\}\) and \(B=\{6,8,10,12\}\), what is \(A\cup B\)?
#sets
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#class11
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A ( {2,4,6,8,10,12} )
B ( {6,8} )
C ( {2,4} )
D ( {10,12} )
Explanation opens after your attempt
Correct Answer
A. ( {2,4,6,8,10,12} )
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. ( {2,4,6,8,10,12} ). \(A\cup B\) 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 अवयवों को केवल एक बार लिखें।
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यदि \(A=\{1,4,7,10\}\) और \(B=\{2,4,6,10\}\) है, तो \(A\cap B\) क्या है?
If \(A=\{1,4,7,10\}\) and \(B=\{2,4,6,10\}\), what is \(A\cap B\)?
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A ( {1,7} )
B ( {4,10} )
C ( {2,6} )
D ( {1,2,4,6,7,10} )
Explanation opens after your attempt
Correct Answer
B. ( {4,10} )
Step 1
Concept
\(A\cap B\) contains only elements present in both sets. Identify common elements carefully.
Step 2
Why this answer is correct
The correct answer is B. ( {4,10} ). \(A\cap B\) contains only elements present in both sets. Identify common elements carefully.
Step 3
Exam Tip
\(A\cap B\) में केवल वे अवयव आते हैं जो दोनों समुच्चयों में हों। सामान्य अवयवों को ध्यान से पहचानें।
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यदि \(A=\{3,6,9,12,15\}\) और \(B=\{6,12,18\}\) है, तो (A-B) क्या होगा?
If \(A=\{3,6,9,12,15\}\) and \(B=\{6,12,18\}\), what is (A-B)?
#sets
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A ( {3,9,15} )
B ( {6,12} )
C ( {18} )
D ( {3,6,9,12,15,18} )
Explanation opens after your attempt
Correct Answer
A. ( {3,9,15} )
Step 1
Concept
(A-B) keeps elements of (A) that are not in (B). Always start from the first set in difference.
Step 2
Why this answer is correct
The correct answer is A. ( {3,9,15} ). (A-B) keeps elements of (A) that are not in (B). Always start from the first set in difference.
Step 3
Exam Tip
(A-B) में (A) के वे अवयव रहते हैं जो (B) में नहीं हैं। अंतर में हमेशा पहले समुच्चय से शुरुआत करें।
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यदि \(A=\{a,c,e,g\}\) और \(B=\{b,c,d,g\}\) है, तो (B-A) क्या है?
If \(A=\{a,c,e,g\}\) and \(B=\{b,c,d,g\}\), what is (B-A)?
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A ( {a,e} )
B ( {c,g} )
C ( {b,d} )
D ( {a,b,c,d,e,g} )
Explanation opens after your attempt
Correct Answer
C. ( {b,d} )
Step 1
Concept
(B-A) leaves (b) and (d) because they are not in (A). Do not assume (A-B) and (B-A) are the same.
Step 2
Why this answer is correct
The correct answer is C. ( {b,d} ). (B-A) leaves (b) and (d) because they are not in (A). Do not assume (A-B) and (B-A) are the same.
Step 3
Exam Tip
(B-A) में (B) के (b) और (d) बचते हैं क्योंकि ये (A) में नहीं हैं। (A-B) और (B-A) को समान न मानें।
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यदि \(A={x:x\in \mathbb{N},x\le 4}\) और \(B=\{3,4,5,6\}\) है, तो \(A\cup B\) क्या है?
If \(A={x:x\in \mathbb{N},x\le 4}\) and \(B=\{3,4,5,6\}\), what is \(A\cup B\)?
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A ( {1,2,3,4,5,6} )
B ( {3,4} )
C ( {1,2} )
D ( {5,6} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,4,5,6} )
Step 1
Concept
Here \(A=\{1,2,3,4\}\), and (5) and (6) from (B) are also included. First convert the set to roster form.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,4,5,6} ). Here \(A=\{1,2,3,4\}\), and (5) and (6) from (B) are also included. First convert the set to roster form.
Step 3
Exam Tip
यहां \(A=\{1,2,3,4\}\) है और संघ में (B) के (5) और (6) भी जुड़ते हैं। पहले समुच्चय को सूची रूप में बदलें।
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यदि \(A=\{2,4,6\}\) और \(B=\{1,3,5\}\) है, तो \(A\cap B\) क्या है?
If \(A=\{2,4,6\}\) and \(B=\{1,3,5\}\), what is \(A\cap B\)?
#sets
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A ( {1,2,3,4,5,6} )
B ( {2,4,6} )
C \( \varnothing \)
D ( {1,3,5} )
Explanation opens after your attempt
Correct Answer
C. \( \varnothing \)
Step 1
Concept
There is no common element, so \(A\cap B=\varnothing\). Disjoint sets have an empty intersection.
Step 2
Why this answer is correct
The correct answer is C. \( \varnothing \). There is no common element, so \(A\cap B=\varnothing\). Disjoint sets have an empty intersection.
Step 3
Exam Tip
दोनों समुच्चयों में कोई समान अवयव नहीं है इसलिए \(A\cap B=\varnothing\) है। असंयुक्त समुच्चयों का प्रतिच्छेद रिक्त होता है।
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यदि \(A=\{r,s\}\) और \(B=\{r,s,t,u\}\) है, तो \(A\cup B\) क्या होगा?
If \(A=\{r,s\}\) and \(B=\{r,s,t,u\}\), what is \(A\cup B\)?
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#subset
#union
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A ( {r,s} )
B ( {t,u} )
C ( {r,s,t,u} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
C. ( {r,s,t,u} )
Step 1
Concept
Since \(A\subseteq B\), \(A\cup B=B\). In subset cases, the larger set is the union.
Step 2
Why this answer is correct
The correct answer is C. ( {r,s,t,u} ). Since \(A\subseteq B\), \(A\cup B=B\). In subset cases, the larger set is the union.
Step 3
Exam Tip
क्योंकि \(A\subseteq B\), इसलिए \(A\cup B=B\) है। उपसमुच्चय वाले प्रश्नों में बड़ा समुच्चय संघ होता है।
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यदि \(A=\{5,10,15,20\}\) और \(B=\{10,20\}\) है, तो \(A\cap B\) क्या है?
If \(A=\{5,10,15,20\}\) and \(B=\{10,20\}\), what is \(A\cap B\)?
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A ( {5,15} )
B ( {10,20} )
C ( {5,10,15,20} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
B. ( {10,20} )
Step 1
Concept
Here \(B\subseteq A\), so \(A\cap B=B\). In subset cases, intersection gives the smaller set.
Step 2
Why this answer is correct
The correct answer is B. ( {10,20} ). Here \(B\subseteq A\), so \(A\cap B=B\). In subset cases, intersection gives the smaller set.
Step 3
Exam Tip
यहां \(B\subseteq A\), इसलिए \(A\cap B=B\) है। उपसमुच्चय में प्रतिच्छेद छोटा समुच्चय देता है।
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यदि \(A=\{11,22,33\}\) है, तो \(A\cup \varnothing\) क्या है?
If \(A=\{11,22,33\}\), what is \(A\cup \varnothing\)?
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#emptyset
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#identity
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A \( \varnothing \)
B ( {11,22,33} )
C ( {0} )
D ( {11} )
Explanation opens after your attempt
Correct Answer
B. ( {11,22,33} )
Step 1
Concept
The empty set has no element, so \(A\cup \varnothing=A\). This is a basic identity of union.
Step 2
Why this answer is correct
The correct answer is B. ( {11,22,33} ). The empty set has no element, so \(A\cup \varnothing=A\). This is a basic identity of union.
Step 3
Exam Tip
रिक्त समुच्चय में कोई अवयव नहीं होता इसलिए \(A\cup \varnothing=A\) है। यह संघ का मूल पहचान सूत्र है।
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यदि \(A=\{2,3,5,7\}\) है, तो \(A\cap \varnothing\) क्या होगा?
If \(A=\{2,3,5,7\}\), what is \(A\cap \varnothing\)?
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A ( {2,3,5,7} )
B ( {0} )
C \( \varnothing \)
D ( {2} )
Explanation opens after your attempt
Correct Answer
C. \( \varnothing \)
Step 1
Concept
Since \(\varnothing\) has no element, there is no common element. Always \(A\cap \varnothing=\varnothing\).
Step 2
Why this answer is correct
The correct answer is C. \( \varnothing \). Since \(\varnothing\) has no element, there is no common element. Always \(A\cap \varnothing=\varnothing\).
Step 3
Exam Tip
\(\varnothing\) में कोई अवयव नहीं है, इसलिए सामान्य अवयव भी नहीं होगा। हमेशा \(A\cap \varnothing=\varnothing\) होता है।
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यदि \(A=\{9,18,27\}\) है, तो \(A-\varnothing\) क्या है?
If \(A=\{9,18,27\}\), what is \(A-\varnothing\)?
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A ( {9,18,27} )
B \( \varnothing \)
C ( {0} )
D ( {18} )
Explanation opens after your attempt
Correct Answer
A. ( {9,18,27} )
Step 1
Concept
There is no element in \(\varnothing\) to remove, so \(A-\varnothing=A\). In difference, check the removing set carefully.
Step 2
Why this answer is correct
The correct answer is A. ( {9,18,27} ). There is no element in \(\varnothing\) to remove, so \(A-\varnothing=A\). In difference, check the removing set carefully.
Step 3
Exam Tip
\(\varnothing\) से कोई अवयव हटाने के लिए नहीं है, इसलिए \(A-\varnothing=A\) है। अंतर में हटाए जाने वाले समुच्चय को ध्यान से देखें।
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यदि \(A=\{4,5,6\}\) है, तो \(\varnothing-A\) क्या है?
If \(A=\{4,5,6\}\), what is \(\varnothing-A\)?
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A ( {4,5,6} )
B \( \varnothing \)
C ( {0} )
D ( {4} )
Explanation opens after your attempt
Correct Answer
B. \( \varnothing \)
Step 1
Concept
The empty set has no element from the start, so nothing remains. Remember \(\varnothing-A=\varnothing\).
Step 2
Why this answer is correct
The correct answer is B. \( \varnothing \). The empty set has no element from the start, so nothing remains. Remember \(\varnothing-A=\varnothing\).
Step 3
Exam Tip
\(\varnothing\) में पहले से कोई अवयव नहीं है, इसलिए कुछ भी नहीं बचेगा। याद रखें \(\varnothing-A=\varnothing\) होता है।
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यदि \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6\}\) है, तो (A-B) और (B-A) का संघ क्या है?
If \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), what is the union of (A-B) and (B-A)?
#sets
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#symmetric
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A ( {1,2,5,6} )
B ( {3,4} )
C ( {1,2,3,4,5,6} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {1,2,5,6} )
Step 1
Concept
(A-B={1,2}) and (B-A={5,6}), so the union is ({1,2,5,6}). It shows the parts outside the common part.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,5,6} ). (A-B={1,2}) and (B-A={5,6}), so the union is ({1,2,5,6}). It shows the parts outside the common part.
Step 3
Exam Tip
(A-B={1,2}) और (B-A={5,6}), इसलिए संघ ({1,2,5,6}) है। यह सामान्य भाग को छोड़कर बचे भागों को दिखाता है।
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यदि (n(A)=14), (n(B)=9) और (n\(A\cap B\)=4) है, तो (n\(A\cup B\)) कितना है?
If (n(A)=14), (n(B)=9), and (n\(A\cap B\)=4), what is (n\(A\cup B\))?
#sets
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A (19)
B (23)
C (27)
D (5)
Explanation opens after your attempt
Step 1
Concept
Using (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)), (14+9-4=19). The common part must be subtracted once.
Step 2
Why this answer is correct
The correct answer is A. (19). Using (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)), (14+9-4=19). The common part must be subtracted once.
Step 3
Exam Tip
सूत्र (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)) से (14+9-4=19) है। सामान्य भाग को एक बार घटाना जरूरी है।
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यदि (n\(A\cup B\)=20), (n(A)=12) और (n(B)=11) है, तो (n\(A\cap B\)) कितना है?
If (n\(A\cup B\)=20), (n(A)=12), and (n(B)=11), what is (n\(A\cap B\))?
#sets
#cardinality
#intersection
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
From the formula, (n\(A\cap B\)=12+11-20=3). When using the formula backward, subtract the union.
Step 2
Why this answer is correct
The correct answer is C. (3). From the formula, (n\(A\cap B\)=12+11-20=3). When using the formula backward, subtract the union.
Step 3
Exam Tip
सूत्र से (n\(A\cap B\)=12+11-20=3) है। उल्टा सूत्र लगाते समय संघ को घटाएं।
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यदि (n(A)=18) और (n\(A\cap B\)=7) है, तो (n(A-B)) कितना होगा?
If (n(A)=18) and (n\(A\cap B\)=7), what is (n(A-B))?
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#cardinality
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#easy
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A (25)
B (18)
C (11)
D (7)
Explanation opens after your attempt
Step 1
Concept
In (A-B), the (7) common elements are removed from (A), so (18-7=11). Count only elements related to (A).
Step 2
Why this answer is correct
The correct answer is C. (11). In (A-B), the (7) common elements are removed from (A), so (18-7=11). Count only elements related to (A).
Step 3
Exam Tip
(A-B) में (A) से सामान्य (7) अवयव हटेंगे, इसलिए (18-7=11) है। केवल (A) से जुड़े अवयव गिनें।
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यदि (n(B)=15) और (n\(A\cap B\)=6) है, तो (n(B-A)) कितना है?
If (n(B)=15) and (n\(A\cap B\)=6), what is (n(B-A))?
#sets
#cardinality
#difference
#easy
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A (9)
B (15)
C (21)
D (6)
Explanation opens after your attempt
Step 1
Concept
For (B-A), the common part is removed from (B), so (15-6=9). In difference, subtract from the first set.
Step 2
Why this answer is correct
The correct answer is A. (9). For (B-A), the common part is removed from (B), so (15-6=9). In difference, subtract from the first set.
Step 3
Exam Tip
(B-A) के लिए (B) से सामान्य भाग हटेगा, इसलिए (15-6=9) है। अंतर में पहले समुच्चय की संख्या से घटाएं।
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यदि \(A={x:x\in \mathbb{N},2\le x\le 7}\) और \(B=\{4,6,8\}\) है, तो (A-B) क्या है?
If \(A={x:x\in \mathbb{N},2\le x\le 7}\) and \(B=\{4,6,8\}\), what is (A-B)?
#sets
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#difference
#easy
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A ( {2,3,5,7} )
B ( {4,6} )
C ( {8} )
D ( {2,3,4,5,6,7,8} )
Explanation opens after your attempt
Correct Answer
A. ( {2,3,5,7} )
Step 1
Concept
\(A=\{2,3,4,5,6,7\}\), and removing (4,6) gives ({2,3,5,7}). First list elements according to the bounds.
Step 2
Why this answer is correct
The correct answer is A. ( {2,3,5,7} ). \(A=\{2,3,4,5,6,7\}\), and removing (4,6) gives ({2,3,5,7}). First list elements according to the bounds.
Step 3
Exam Tip
\(A=\{2,3,4,5,6,7\}\) है और (4,6) हटाने पर ({2,3,5,7}) बचता है। पहले सीमा के अनुसार अवयव लिखें।
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यदि \(A=\{0,1,2,3,4\}\) और \(B=\{2,3,4,5,6\}\) है, तो (\(A\cup B\)-\(A\cap B\)) क्या है?
If \(A=\{0,1,2,3,4\}\) and \(B=\{2,3,4,5,6\}\), what is (\(A\cup B\)-\(A\cap B\))?
#sets
#union
#intersection
#difference
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A ( {0,1,5,6} )
B ( {2,3,4} )
C ( {0,1,2,3,4,5,6} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {0,1,5,6} )
Step 1
Concept
The union is ({0,1,2,3,4,5,6}) and the intersection is ({2,3,4}). Removing the intersection gives ({0,1,5,6}).
Step 2
Why this answer is correct
The correct answer is A. ( {0,1,5,6} ). The union is ({0,1,2,3,4,5,6}) and the intersection is ({2,3,4}). Removing the intersection gives ({0,1,5,6}).
Step 3
Exam Tip
संघ ({0,1,2,3,4,5,6}) और प्रतिच्छेद ({2,3,4}) है। प्रतिच्छेद हटाने पर ({0,1,5,6}) मिलता है।
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कौन सा नियम हमेशा सही है?
Which rule is always true?
#sets
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#union
#concept
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A \(A\cup B=B\cup A\)
B (A-B=B-A)
C \(A\cap \varnothing=A\)
D \(A\cup A=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(A\cup B=B\cup A\)
Step 1
Concept
The order of sets does not change the union. This is the commutative law of union.
Step 2
Why this answer is correct
The correct answer is A. \(A\cup B=B\cup A\). The order of sets does not change the union. This is the commutative law of union.
Step 3
Exam Tip
संघ में समुच्चयों का क्रम बदलने से उत्तर नहीं बदलता। इसे संघ का क्रमविनिमेय नियम कहते हैं।
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यदि \(A=\{2,3,4,5\}\), \(B=\{1,3,5,7\}\) और \(C=\{0,3,6,9\}\) है, तो \(A\cap B\cap C\) क्या है?
If \(A=\{2,3,4,5\}\), \(B=\{1,3,5,7\}\), and \(C=\{0,3,6,9\}\), what is \(A\cap B\cap C\)?
#sets
#three-sets
#intersection
#easy
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A ( {3} )
B ( {5} )
C ( {3,5} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {3} )
Step 1
Concept
Only (3) is present in all three sets. In the intersection of three sets, the element must be in every set.
Step 2
Why this answer is correct
The correct answer is A. ( {3} ). Only (3) is present in all three sets. In the intersection of three sets, the element must be in every set.
Step 3
Exam Tip
केवल (3) तीनों समुच्चयों में मौजूद है। तीन समुच्चयों के प्रतिच्छेद में अवयव सभी में होना चाहिए।
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यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{2,3\}\) और \(C=\{5,6,7\}\) है, तो (A-\(B\cup C\)) क्या है?
If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,3\}\), and \(C=\{5,6,7\}\), what is (A-\(B\cup C\))?
#sets
#difference
#union
#three-sets
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A ( {1,4} )
B ( {2,3,5,6,7} )
C ( {1,2,3,4,5,6} )
D ( {7} )
Explanation opens after your attempt
Correct Answer
A. ( {1,4} )
Step 1
Concept
\(B\cup C={2,3,5,6,7}\), and removing these from (A) leaves ({1,4}). Solve the bracket first.
Step 2
Why this answer is correct
The correct answer is A. ( {1,4} ). \(B\cup C={2,3,5,6,7}\), and removing these from (A) leaves ({1,4}). Solve the bracket first.
Step 3
Exam Tip
\(B\cup C={2,3,5,6,7}\) है और (A) से इन्हें हटाने पर ({1,4}) बचता है। पहले कोष्ठक हल करें।
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यदि \(A=\{a,b,c,d\}\), \(B=\{b,d,f\}\) और \(C=\{d,e,f\}\) है, तो (A\cap\(B\cup C\)) क्या है?
If \(A=\{a,b,c,d\}\), \(B=\{b,d,f\}\), and \(C=\{d,e,f\}\), what is (A\cap\(B\cup C\))?
#sets
#union
#intersection
#three-sets
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A ( {b,d} )
B ( {a,c} )
C ( {e,f} )
D ( {a,b,c,d,e,f} )
Explanation opens after your attempt
Correct Answer
A. ( {b,d} )
Step 1
Concept
\(B\cup C={b,d,e,f}\), and its common part with (A) is ({b,d}). Do combined operations step by step.
Step 2
Why this answer is correct
The correct answer is A. ( {b,d} ). \(B\cup C={b,d,e,f}\), and its common part with (A) is ({b,d}). Do combined operations step by step.
Step 3
Exam Tip
\(B\cup C={b,d,e,f}\) है और इसका (A) से सामान्य भाग ({b,d}) है। संयुक्त क्रियाओं को क्रम से करें।
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यदि \(A=\{1,3,5,7\}\), \(B=\{3,5,9\}\) और \(C=\{5,7,11\}\) है, तो (\(A\cap B\)\cup C) क्या है?
If \(A=\{1,3,5,7\}\), \(B=\{3,5,9\}\), and \(C=\{5,7,11\}\), what is (\(A\cap B\)\cup C)?
#sets
#intersection
#union
#three-sets
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A ( {3,5,7,11} )
B ( {5} )
C ( {1,3,5,7,9,11} )
D ( {3} )
Explanation opens after your attempt
Correct Answer
A. ( {3,5,7,11} )
Step 1
Concept
\(A\cap B={3,5}\), and its union with (C) is ({3,5,7,11}). Perform the operation inside brackets first.
Step 2
Why this answer is correct
The correct answer is A. ( {3,5,7,11} ). \(A\cap B={3,5}\), and its union with (C) is ({3,5,7,11}). Perform the operation inside brackets first.
Step 3
Exam Tip
\(A\cap B={3,5}\) है और (C) के साथ संघ ({3,5,7,11}) है। कोष्ठक वाली क्रिया पहले करें।
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यदि \(A=\{2,4,6,8\}\) और \(B=\{1,2,3,4,5\}\) है, तो \(A\cup B\) में कितने अवयव हैं?
If \(A=\{2,4,6,8\}\) and \(B=\{1,2,3,4,5\}\), how many elements are in \(A\cup B\)?
#sets
#cardinality
#union
#easy
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A (5)
B (6)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B={1,2,3,4,5,6,8}\), so it has (7) elements. Do not count common elements twice.
Step 2
Why this answer is correct
The correct answer is C. (7). \(A\cup B={1,2,3,4,5,6,8}\), so it has (7) elements. Do not count common elements twice.
Step 3
Exam Tip
\(A\cup B={1,2,3,4,5,6,8}\) है, इसलिए इसमें (7) अवयव हैं। सामान्य अवयवों को दो बार न गिनें।
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यदि \(A=\{12,24,36,48\}\) और \(B=\{24,48,60\}\) है, तो \(A\cap B\) में कितने अवयव हैं?
If \(A=\{12,24,36,48\}\) and \(B=\{24,48,60\}\), how many elements are in \(A\cap B\)?
#sets
#cardinality
#intersection
#easy
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The common elements are (24) and (48), so the count is (2). In intersection, count only common elements.
Step 2
Why this answer is correct
The correct answer is B. (2). The common elements are (24) and (48), so the count is (2). In intersection, count only common elements.
Step 3
Exam Tip
सामान्य अवयव (24) और (48) हैं, इसलिए संख्या (2) है। प्रतिच्छेद में केवल समान अवयव गिने जाते हैं।
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यदि \(A=\{1,8,27,64\}\) और \(B=\{8,64,125\}\) है, तो (A-B) क्या है?
If \(A=\{1,8,27,64\}\) and \(B=\{8,64,125\}\), what is (A-B)?
#sets
#difference
#cubes
#easy
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A ( {1,27} )
B ( {8,64} )
C ( {125} )
D ( {1,8,27,64,125} )
Explanation opens after your attempt
Correct Answer
A. ( {1,27} )
Step 1
Concept
The elements (8) and (64) are removed from (A) because they are also in (B). So (A-B={1,27}).
Step 2
Why this answer is correct
The correct answer is A. ( {1,27} ). The elements (8) and (64) are removed from (A) because they are also in (B). So (A-B={1,27}).
Step 3
Exam Tip
(A) से (8) और (64) हटेंगे क्योंकि वे (B) में भी हैं। इसलिए (A-B={1,27}) है।
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यदि \(A=\{1,2,3,4,5\}\) और \(B=\{6,7,8\}\) है, तो (A-B) क्या होगा?
If \(A=\{1,2,3,4,5\}\) and \(B=\{6,7,8\}\), what is (A-B)?
#sets
#disjoint
#difference
#easy
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A \( \varnothing \)
B ( {1,2,3,4,5} )
C ( {6,7,8} )
D ( {1,2,3,4,5,6,7,8} )
Explanation opens after your attempt
Correct Answer
B. ( {1,2,3,4,5} )
Step 1
Concept
The two sets are disjoint, so no element is removed from (A). For disjoint sets, (A-B=A).
Step 2
Why this answer is correct
The correct answer is B. ( {1,2,3,4,5} ). The two sets are disjoint, so no element is removed from (A). For disjoint sets, (A-B=A).
Step 3
Exam Tip
दोनों समुच्चय असंयुक्त हैं, इसलिए (A) से कोई अवयव नहीं हटेगा। असंयुक्त समुच्चयों के लिए (A-B=A) होता है।
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यदि \(A=\{pen,book,bag\}\) और \(B=\{book,desk\}\) है, तो \(A\cap B\) क्या है?
If \(A=\{pen,book,bag\}\) and \(B=\{book,desk\}\), what is \(A\cap B\)?
#sets
#word-set
#intersection
#easy
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A ( {pen,bag} )
B ( {book} )
C ( {desk} )
D ( {pen,book,bag,desk} )
Explanation opens after your attempt
Correct Answer
B. ( {book} )
Step 1
Concept
Only (book) is common to both sets. Write only common elements in the intersection.
Step 2
Why this answer is correct
The correct answer is B. ( {book} ). Only (book) is common to both sets. Write only common elements in the intersection.
Step 3
Exam Tip
दोनों समुच्चयों में केवल (book) समान है। प्रतिच्छेद में केवल समान अवयव लिखें।
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यदि \(A=\{rose,lily\}\) और \(B=\{lily,lotus,jasmine\}\) है, तो \(A\cup B\) क्या है?
If \(A=\{rose,lily\}\) and \(B=\{lily,lotus,jasmine\}\), what is \(A\cup B\)?
#sets
#word-set
#union
#easy
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A ( {rose,lily,lotus,jasmine} )
B ( {lily} )
C ( {rose} )
D ( {lotus,jasmine} )
Explanation opens after your attempt
Correct Answer
A. ( {rose,lily,lotus,jasmine} )
Step 1
Concept
The union contains all distinct names, so (lily) is written once. The answer is ({rose,lily,lotus,jasmine}).
Step 2
Why this answer is correct
The correct answer is A. ( {rose,lily,lotus,jasmine} ). The union contains all distinct names, so (lily) is written once. The answer is ({rose,lily,lotus,jasmine}).
Step 3
Exam Tip
संघ में सभी अलग-अलग नाम आते हैं, इसलिए (lily) एक बार लिखा जाएगा। उत्तर ({rose,lily,lotus,jasmine}) है।
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यदि \(A=\{north,south,east,west\}\) और \(B=\{east,west\}\) है, तो (A-B) क्या है?
If \(A=\{north,south,east,west\}\) and \(B=\{east,west\}\), what is (A-B)?
#sets
#word-set
#difference
#easy
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A ( {north,south} )
B ( {east,west} )
C \( \varnothing \)
D ( {north,south,east,west} )
Explanation opens after your attempt
Correct Answer
A. ( {north,south} )
Step 1
Concept
Removing (east) and (west) from (A) leaves (north) and (south). Removed elements do not appear in the difference.
Step 2
Why this answer is correct
The correct answer is A. ( {north,south} ). Removing (east) and (west) from (A) leaves (north) and (south). Removed elements do not appear in the difference.
Step 3
Exam Tip
(A) से (east) और (west) हटाने पर (north) और (south) बचते हैं। अंतर में हटाए गए अवयव उत्तर में नहीं आते।
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यदि \(A=\{2,4,6,8\}\) और \(B=\{4,8,12\}\) है, तो कौन सा अवयव \(A\cap B\) में है?
If \(A=\{2,4,6,8\}\) and \(B=\{4,8,12\}\), which element is in \(A\cap B\)?
#sets
#membership
#intersection
#easy
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A (2)
B (4)
C (6)
D (12)
Explanation opens after your attempt
Step 1
Concept
(4) is in both sets, so it is in \(A\cap B\). For intersection, an element must be in both sets.
Step 2
Why this answer is correct
The correct answer is B. (4). (4) is in both sets, so it is in \(A\cap B\). For intersection, an element must be in both sets.
Step 3
Exam Tip
(4) दोनों समुच्चयों में है, इसलिए वह \(A\cap B\) में है। प्रतिच्छेद के लिए अवयव दोनों में होना चाहिए।
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यदि \(A=\{3,6,9\}\) और \(B=\{9,12,15\}\) है, तो कौन सा अवयव \(A\cup B\) में अवश्य होगा?
If \(A=\{3,6,9\}\) and \(B=\{9,12,15\}\), which element must belong to \(A\cup B\)?
#sets
#membership
#union
#easy
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A (6)
B (18)
C (21)
D (0)
Explanation opens after your attempt
Step 1
Concept
(6) is in set (A), so it is also in \(A\cup B\). A union includes elements from either set.
Step 2
Why this answer is correct
The correct answer is A. (6). (6) is in set (A), so it is also in \(A\cup B\). A union includes elements from either set.
Step 3
Exam Tip
(6) समुच्चय (A) में है, इसलिए \(A\cup B\) में भी होगा। संघ में किसी भी एक समुच्चय का अवयव शामिल होता है।
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यदि \(A=\{1,2,5,10\}\) और \(B=\{2,4,6,10\}\) है, तो कौन सा अवयव (A-B) में है?
If \(A=\{1,2,5,10\}\) and \(B=\{2,4,6,10\}\), which element is in (A-B)?
#sets
#membership
#difference
#easy
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A (1)
B (2)
C (4)
D (10)
Explanation opens after your attempt
Step 1
Concept
(1) is in (A) but not in (B), so \(1\in A-B\). Difference keeps non-common elements of the first set.
Step 2
Why this answer is correct
The correct answer is A. (1). (1) is in (A) but not in (B), so \(1\in A-B\). Difference keeps non-common elements of the first set.
Step 3
Exam Tip
(1) (A) में है लेकिन (B) में नहीं है, इसलिए \(1\in A-B\) है। अंतर में पहले समुच्चय के गैर-सामान्य अवयव रहते हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,7\}\) और \(B=\{2,4,6\}\) है, तो \(A\cup B\) क्या है?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,7\}\), and \(B=\{2,4,6\}\), what is \(A\cup B\)?
#sets
#universal-set
#union
#easy
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A ( {1,2,4,6,7} )
B ( {3,5,8} )
C ( {2} )
D ( {1,2,3,4,5,6,7,8} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,4,6,7} )
Step 1
Concept
\(A\cup B\) contains all distinct elements of (A) and (B). (U) is only the universal set; the answer is not always the whole (U).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,4,6,7} ). \(A\cup B\) contains all distinct elements of (A) and (B). (U) is only the universal set; the answer is not always the whole (U).
Step 3
Exam Tip
\(A\cup B\) में (A) और (B) के सभी अलग-अलग अवयव हैं। (U) केवल सार्वत्रिक समुच्चय है, उत्तर हमेशा पूरा (U) नहीं होता।
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यदि \(U=\{a,b,c,d,e,f\}\), \(A=\{a,c,e\}\) और \(B=\{b,c,e,f\}\) है, तो \(A\cap B\) क्या है?
If \(U=\{a,b,c,d,e,f\}\), \(A=\{a,c,e\}\), and \(B=\{b,c,e,f\}\), what is \(A\cap B\)?
#sets
#universal-set
#intersection
#easy
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A ( {c,e} )
B ( {a} )
C ( {b,f} )
D ( {a,b,c,d,e,f} )
Explanation opens after your attempt
Correct Answer
A. ( {c,e} )
Step 1
Concept
The common elements of (A) and (B) are (c) and (e). The universal set only gives the reference.
Step 2
Why this answer is correct
The correct answer is A. ( {c,e} ). The common elements of (A) and (B) are (c) and (e). The universal set only gives the reference.
Step 3
Exam Tip
(A) और (B) में सामान्य अवयव (c) और (e) हैं। सार्वत्रिक समुच्चय केवल संदर्भ देता है।
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यदि \(U=\{10,20,30,40,50\}\), \(A=\{10,20,40\}\) और \(B=\{20,30\}\) है, तो (A-B) क्या है?
If \(U=\{10,20,30,40,50\}\), \(A=\{10,20,40\}\), and \(B=\{20,30\}\), what is (A-B)?
#sets
#universal-set
#difference
#easy
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A ( {10,40} )
B ( {20} )
C ( {30,50} )
D ( {10,20,30,40,50} )
Explanation opens after your attempt
Correct Answer
A. ( {10,40} )
Step 1
Concept
The common element (20) is removed from (A), leaving ({10,40}). Even when (U) is given, find the difference from (A) and (B).
Step 2
Why this answer is correct
The correct answer is A. ( {10,40} ). The common element (20) is removed from (A), leaving ({10,40}). Even when (U) is given, find the difference from (A) and (B).
Step 3
Exam Tip
(A) से (B) का समान अवयव (20) हटता है और ({10,40}) बचता है। (U) दिए होने पर भी अंतर (A) और (B) से निकालें।
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यदि \(A=\{1,2,3,4\}\) और \(B=\{2,4,6\}\) है, तो \(A\cap(A-B)\) क्या है?
If \(A=\{1,2,3,4\}\) and \(B=\{2,4,6\}\), what is \(A\cap(A-B)\)?
#sets
#difference
#intersection
#identity
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A ( {1,3} )
B ( {2,4} )
C ( {6} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {1,3} )
Step 1
Concept
First (A-B={1,3}), and it is a part of (A). Therefore \(A\cap(A-B)={1,3}\).
Step 2
Why this answer is correct
The correct answer is A. ( {1,3} ). First (A-B={1,3}), and it is a part of (A). Therefore \(A\cap(A-B)={1,3}\).
Step 3
Exam Tip
पहले (A-B={1,3}) है और यह (A) का भाग है। इसलिए \(A\cap(A-B)={1,3}\) है।
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यदि \(A=\{5,6,7\}\) और \(B=\{6,7,8,9\}\) है, तो (A\cap\(A\cup B\)) क्या है?
If \(A=\{5,6,7\}\) and \(B=\{6,7,8,9\}\), what is (A\cap\(A\cup B\))?
#sets
#absorption
#intersection
#union
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A ( {5,6,7} )
B ( {6,7} )
C ( {5,6,7,8,9} )
D ( {8,9} )
Explanation opens after your attempt
Correct Answer
A. ( {5,6,7} )
Step 1
Concept
\(A\cup B\) contains all elements of (A), so the intersection is (A) itself. This is an example of the absorption law.
Step 2
Why this answer is correct
The correct answer is A. ( {5,6,7} ). \(A\cup B\) contains all elements of (A), so the intersection is (A) itself. This is an example of the absorption law.
Step 3
Exam Tip
\(A\cup B\) में (A) के सभी अवयव हैं, इसलिए प्रतिच्छेद (A) ही होगा। यह अवशोषण नियम का उदाहरण है।
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यदि \(A=\{p,q,r\}\) और \(B=\{q,r,s\}\) है, तो (A\cup\(A\cap B\)) क्या है?
If \(A=\{p,q,r\}\) and \(B=\{q,r,s\}\), what is (A\cup\(A\cap B\))?
#sets
#absorption
#union
#intersection
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A ( {p,q,r} )
B ( {q,r} )
C ( {p,q,r,s} )
D ( {s} )
Explanation opens after your attempt
Correct Answer
A. ( {p,q,r} )
Step 1
Concept
\(A\cap B={q,r}\), and it is a part of (A), so the union is (A) itself. This is the absorption law.
Step 2
Why this answer is correct
The correct answer is A. ( {p,q,r} ). \(A\cap B={q,r}\), and it is a part of (A), so the union is (A) itself. This is the absorption law.
Step 3
Exam Tip
\(A\cap B={q,r}\) है और यह (A) का भाग है, इसलिए संघ (A) ही होगा। यह अवशोषण नियम है।
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एक कक्षा में (22) विद्यार्थी चित्रकला पसंद करते हैं, (16) संगीत पसंद करते हैं और (6) दोनों पसंद करते हैं। कम से कम एक गतिविधि पसंद करने वाले कितने विद्यार्थी हैं?
In a class, (22) students like drawing, (16) like music, and (6) like both. How many students like at least one activity?
#sets
#word-problem
#union
#cardinality
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A (32)
B (38)
C (44)
D (12)
Explanation opens after your attempt
Step 1
Concept
At least one means (n\(A\cup B\)), so (22+16-6=32). Do not count those who like both twice.
Step 2
Why this answer is correct
The correct answer is A. (32). At least one means (n\(A\cup B\)), so (22+16-6=32). Do not count those who like both twice.
Step 3
Exam Tip
कम से कम एक का अर्थ (n\(A\cup B\)) है, इसलिए (22+16-6=32) है। दोनों पसंद करने वालों को दो बार न गिनें।
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एक समूह में (30) विद्यार्थी चाय पसंद करते हैं, (25) कॉफी पसंद करते हैं और (12) दोनों पसंद करते हैं। केवल चाय पसंद करने वाले कितने हैं?
In a group, (30) students like tea, (25) like coffee, and (12) like both. How many like only tea?
#sets
#word-problem
#difference
#easy
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A (18)
B (13)
C (43)
D (55)
Explanation opens after your attempt
Step 1
Concept
Only tea is (30-12=18). In only-type questions, subtract the intersection from that set.
Step 2
Why this answer is correct
The correct answer is A. (18). Only tea is (30-12=18). In only-type questions, subtract the intersection from that set.
Step 3
Exam Tip
केवल चाय (=30-12=18) है। केवल वाले प्रश्न में उसी समुच्चय से प्रतिच्छेद घटाएं।
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एक सर्वे में (28) विद्यार्थी बस से आते हैं, (14) साइकिल से आते हैं और (9) दोनों तरीकों का उपयोग करते हैं। केवल साइकिल का उपयोग करने वाले कितने हैं?
In a survey, (28) students use bus, (14) use bicycle, and (9) use both methods. How many use only bicycle?
#sets
#word-problem
#difference
#easy
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A (5)
B (19)
C (23)
D (42)
Explanation opens after your attempt
Step 1
Concept
Only bicycle is (14-9=5). For only the second set, subtract the common part from the second set.
Step 2
Why this answer is correct
The correct answer is A. (5). Only bicycle is (14-9=5). For only the second set, subtract the common part from the second set.
Step 3
Exam Tip
केवल साइकिल (=14-9=5) है। केवल दूसरे समुच्चय के लिए दूसरे समुच्चय से सामान्य भाग घटाएं।
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\(यदि (A={x:x\in \mathbb{N},x\) is a factor of \(12}) और (B={1,2,3,5}) है, तो (A\cap B) क्या है\)?
\(If (A={x:x\in \mathbb{N},x\) is a factor of \(12}) and (B={1,2,3,5}), what is (A\cap B)\)?
#sets
#factors
#intersection
#easy
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A ( {1,2,3} )
B ( {1,2,3,4,6,12} )
C ( {5} )
D ( {4,6,12} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3} )
Step 1
Concept
\(A=\{1,2,3,4,6,12\}\), and the common part with (B) is ({1,2,3}). List the factor set first.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3} ). \(A=\{1,2,3,4,6,12\}\), and the common part with (B) is ({1,2,3}). List the factor set first.
Step 3
Exam Tip
\(A=\{1,2,3,4,6,12\}\) है और (B) के साथ सामान्य भाग ({1,2,3}) है। गुणनखंड वाले समुच्चय को पहले लिखें।
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\(यदि (A={x:x\in \mathbb{N},x\) is a factor of \(18}) और (B={2,3,6,9}) है, तो (A-B) क्या है\)?
\(If (A={x:x\in \mathbb{N},x\) is a factor of \(18}) and (B={2,3,6,9}), what is (A-B)\)?
#sets
#factors
#difference
#easy
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A ( {1,18} )
B ( {2,3,6,9} )
C ( {1,2,3,6,9,18} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {1,18} )
Step 1
Concept
\(A=\{1,2,3,6,9,18\}\), and removing (B) leaves ({1,18}). Converting to roster form reduces mistakes.
Step 2
Why this answer is correct
The correct answer is A. ( {1,18} ). \(A=\{1,2,3,6,9,18\}\), and removing (B) leaves ({1,18}). Converting to roster form reduces mistakes.
Step 3
Exam Tip
\(A=\{1,2,3,6,9,18\}\) है और (B) हटाने पर ({1,18}) बचता है। सूची रूप में बदलने से गलती कम होती है।
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यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{2,3,5\}\) और \(C=\{3,4,6\}\) है, तो \((A-B)\cap C\) क्या है?
If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,3,5\}\), and \(C=\{3,4,6\}\), what is \((A-B)\cap C\)?
#sets
#difference
#intersection
#three-sets
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A ( {4,6} )
B ( {3} )
C ( {1,4,6} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {4,6} )
Step 1
Concept
First (A-B={1,4,6}), and its common part with (C) is ({4,6}). In mixed operations, solve the bracket first.
Step 2
Why this answer is correct
The correct answer is A. ( {4,6} ). First (A-B={1,4,6}), and its common part with (C) is ({4,6}). In mixed operations, solve the bracket first.
Step 3
Exam Tip
पहले (A-B={1,4,6}) है और इसका (C) से सामान्य भाग ({4,6}) है। मिश्रित क्रियाओं में कोष्ठक पहले हल करें।
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यदि \(A=\{1,2,4,6\}\), \(B=\{2,3,6,8\}\) और \(C=\{2,6,9\}\) है, तो (\(A\cup B\)\cap C) क्या है?
If \(A=\{1,2,4,6\}\), \(B=\{2,3,6,8\}\), and \(C=\{2,6,9\}\), what is (\(A\cup B\)\cap C)?
#sets
#union
#intersection
#three-sets
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A ( {1,3,4,8} )
B ( {2,6} )
C ( {9} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
B. ( {2,6} )
Step 1
Concept
First \(A\cup B={1,2,3,4,6,8}\), then the common part with (C) is ({2,6}). In mixed operations, solve the bracket first.
Step 2
Why this answer is correct
The correct answer is B. ( {2,6} ). First \(A\cup B={1,2,3,4,6,8}\), then the common part with (C) is ({2,6}). In mixed operations, solve the bracket first.
Step 3
Exam Tip
पहले \(A\cup B={1,2,3,4,6,8}\) है, फिर (C) के साथ सामान्य भाग ({2,6}) मिलता है। मिश्रित क्रिया में कोष्ठक पहले हल करें।
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यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6,8\}\) और \(C=\{1,4,6\}\) है, तो (A-\(B\cap C\)) क्या है?
If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6,8\}\), and \(C=\{1,4,6\}\), what is (A-\(B\cap C\))?
#sets
#intersection
#difference
#three-sets
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A ( {1,2,3,5} )
B ( {4,6} )
C ( {1,4,6} )
D ( {2,4,6,8} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,5} )
Step 1
Concept
First \(B\cap C={4,6}\), then removing these from (A) leaves ({1,2,3,5}). In difference, remove elements only from the first set.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,5} ). First \(B\cap C={4,6}\), then removing these from (A) leaves ({1,2,3,5}). In difference, remove elements only from the first set.
Step 3
Exam Tip
पहले \(B\cap C={4,6}\) है, फिर (A) से इन्हें हटाने पर ({1,2,3,5}) बचता है। अंतर में पहले समुच्चय से ही अवयव हटाएं।
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एक पुस्तकालय में (35) विद्यार्थी कहानी की किताबें पढ़ते हैं, (20) विद्यार्थी कविता की किताबें पढ़ते हैं और (45) विद्यार्थी कम से कम एक प्रकार की किताब पढ़ते हैं। दोनों प्रकार की किताबें पढ़ने वाले कितने हैं?
In a library, (35) students read story books, (20) students read poetry books, and (45) students read at least one type of book. How many read both types of books?
#sets
#word-problem
#cardinality
#intersection
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A (5)
B (10)
C (15)
D (55)
Explanation opens after your attempt
Step 1
Concept
Using the formula, (n\(A\cap B\)=35+20-45=10). At least one means (n\(A\cup B\)).
Step 2
Why this answer is correct
The correct answer is B. (10). Using the formula, (n\(A\cap B\)=35+20-45=10). At least one means (n\(A\cup B\)).
Step 3
Exam Tip
सूत्र से (n\(A\cap B\)=35+20-45=10) है। कम से कम एक का अर्थ (n\(A\cup B\)) होता है।
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यदि \(A=\{3,6,9,12\}\) और \(B=\{6,12,18,24\}\) है, तो \((A-B)\cap(B-A)\) क्या है?
If \(A=\{3,6,9,12\}\) and \(B=\{6,12,18,24\}\), what is \((A-B)\cap(B-A)\)?
#sets
#difference
#intersection
#reasoning
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A ( {3,9,18,24} )
B ( {6,12} )
C \( \varnothing \)
D ( {3,9} )
Explanation opens after your attempt
Correct Answer
C. \( \varnothing \)
Step 1
Concept
(A-B={3,9}) and (B-A={18,24}), and they have no common element. Therefore their intersection is \(\varnothing\).
Step 2
Why this answer is correct
The correct answer is C. \( \varnothing \). (A-B={3,9}) and (B-A={18,24}), and they have no common element. Therefore their intersection is \(\varnothing\).
Step 3
Exam Tip
(A-B={3,9}) और (B-A={18,24}) हैं, जिनमें कोई समान अवयव नहीं है। इसलिए उनका प्रतिच्छेद \(\varnothing\) है।
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