यदि \(U=\{2,3,4,5,6\}\) और \(A=\{3,6\}\) है, तो \(A^c\) क्या है?
If \(U=\{2,3,4,5,6\}\) and \(A=\{3,6\}\), what is \(A^c\)?
#sets
#complement
#basic
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A ({2,4,5})
B ({3,6})
C ({2,3,6})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({2,4,5})
Step 1
Concept
\(A^c\) contains the elements of (U) that are not in (A). In exams, cross out the elements of (A) from (U).
Step 2
Why this answer is correct
The correct answer is A. ({2,4,5}). \(A^c\) contains the elements of (U) that are not in (A). In exams, cross out the elements of (A) from (U).
Step 3
Exam Tip
\(A^c\) में (U) के वे तत्व आते हैं जो (A) में नहीं हैं। परीक्षा में (U) से (A) के तत्व काट दें।
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यदि \(U=\{p,q,r,s,t\}\) और \(A=\{p,s,t\}\) है, तो \(A^c\) ज्ञात कीजिए।
If \(U=\{p,q,r,s,t\}\) and \(A=\{p,s,t\}\), find \(A^c\).
#sets
#complement
#letters
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A ({q,r})
B ({p,s,t})
C ({p,q,r})
D ({s,t})
Explanation opens after your attempt
Correct Answer
A. ({q,r})
Step 1
Concept
(A) has (p,s,t), so (q,r) are left. Always write the complement only inside the given (U).
Step 2
Why this answer is correct
The correct answer is A. ({q,r}). (A) has (p,s,t), so (q,r) are left. Always write the complement only inside the given (U).
Step 3
Exam Tip
(A) में (p,s,t) हैं, इसलिए (q,r) बचे हैं। पूरक हमेशा दिए हुए (U) के अंदर ही लिखें।
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यदि \(x\in A^c\) है, तो कौन सा कथन निश्चित रूप से सही है?
If \(x\in A^c\), which statement is definitely true?
#sets
#complement
#membership
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A \(x\in U\) और \(x\notin A\) / \(x\in U\) and \(x\notin A\)
B \(x\in A\) और \(x\in U\) / \(x\in A\) and \(x\in U\)
C \(x\notin U\)
D \(x\in A\cap A^c\)
Explanation opens after your attempt
Correct Answer
A. \(x\in U\) और \(x\notin A\) / \(x\in U\) and \(x\notin A\)
Step 1
Concept
An element of the complement is in (U) but not in (A). In membership questions, check both conditions together.
Step 2
Why this answer is correct
The correct answer is A. \(x\in U\) और \(x\notin A\) / \(x\in U\) and \(x\notin A\). An element of the complement is in (U) but not in (A). In membership questions, check both conditions together.
Step 3
Exam Tip
पूरक का तत्व (U) में होता है पर (A) में नहीं होता। सदस्यता वाले प्रश्नों में दोनों शर्तें साथ जांचें।
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यदि \(U=\{5,10,15,20\}\) और (A=U) है, तो \(A^c\) क्या होगा?
If \(U=\{5,10,15,20\}\) and (A=U), what will \(A^c\) be?
#sets
#complement
#universal
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A \(\varnothing\) / empty set
B (U) / universal set
C ({5,10})
D ({15,20})
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\) / empty set
Step 1
Concept
When (A=U), no element of (U) remains outside (A). Hence \(A^c=\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\) / empty set. When (A=U), no element of (U) remains outside (A). Hence \(A^c=\varnothing\).
Step 3
Exam Tip
जब (A=U) हो, तो (U) में (A) से बाहर कोई तत्व नहीं बचता। इसलिए \(A^c=\varnothing\) होता है।
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यदि \(U=\{7,8,9\}\) और \(A=\varnothing\) है, तो \(A^c\) क्या होगा?
If \(U=\{7,8,9\}\) and \(A=\varnothing\), what will \(A^c\) be?
#sets
#complement
#empty_set
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A (U) / universal set
B \(\varnothing\) / empty set
C ({7})
D ({8,9})
Explanation opens after your attempt
Correct Answer
A. (U) / universal set
Step 1
Concept
No element is removed from \(\varnothing\), so the whole (U) comes in the complement. Remember that \(\varnothing^c=U\).
Step 2
Why this answer is correct
The correct answer is A. (U) / universal set. No element is removed from \(\varnothing\), so the whole (U) comes in the complement. Remember that \(\varnothing^c=U\).
Step 3
Exam Tip
\(\varnothing\) से कोई तत्व नहीं हटता, इसलिए पूरा (U) पूरक में आता है। याद रखें कि \(\varnothing^c=U\) होता है।
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यदि (n(U)=36) और (n(A)=14) है, तो (n\(A^c\)) कितना होगा?
If (n(U)=36) and (n(A)=14), what is (n\(A^c\))?
#sets
#complement
#cardinality
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A (22)
B (50)
C (14)
D (36)
Explanation opens after your attempt
Step 1
Concept
(n\(A^c\)=n(U)-n(A)). Therefore (36-14=22) is correct.
Step 2
Why this answer is correct
The correct answer is A. (22). (n\(A^c\)=n(U)-n(A)). Therefore (36-14=22) is correct.
Step 3
Exam Tip
(n\(A^c\)=n(U)-n(A)) होता है। इसलिए (36-14=22) सही है।
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यदि \(U=\{1,2,3,4,5,6,7\}\) और \(A^c={1,7}\) है, तो (A) क्या होगा?
If \(U=\{1,2,3,4,5,6,7\}\) and \(A^c={1,7}\), what is (A)?
#sets
#complement
#reverse
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A ({2,3,4,5,6})
B ({1,7})
C ({1,2,7})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({2,3,4,5,6})
Step 1
Concept
(A) contains the elements of (U) that are not in \(A^c\). So remove (1) and (7) and write the remaining elements.
Step 2
Why this answer is correct
The correct answer is A. ({2,3,4,5,6}). (A) contains the elements of (U) that are not in \(A^c\). So remove (1) and (7) and write the remaining elements.
Step 3
Exam Tip
(A) में (U) के वे तत्व होंगे जो \(A^c\) में नहीं हैं। इसलिए (1) और (7) हटाकर बाकी तत्व लिखें।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\) और \(A=\{1,3,5,7\}\) है, तो \(A^c\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{1,3,5,7\}\), what is \(A^c\)?
#sets
#complement
#odd_even
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A ({2,4,6,8})
B ({1,3,5,7})
C ({1,2,3,4})
D ({5,6,7,8})
Explanation opens after your attempt
Correct Answer
A. ({2,4,6,8})
Step 1
Concept
(A) contains odd numbers, so \(A^c\) contains even numbers. Identifying the pattern gives the answer quickly.
Step 2
Why this answer is correct
The correct answer is A. ({2,4,6,8}). (A) contains odd numbers, so \(A^c\) contains even numbers. Identifying the pattern gives the answer quickly.
Step 3
Exam Tip
(A) में विषम संख्याएं हैं, इसलिए \(A^c\) में सम संख्याएं आएंगी। पैटर्न पहचानकर उत्तर जल्दी मिलता है।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\) और \(A=\{1,4,9\}\) है, तो \(A^c\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(A=\{1,4,9\}\), what is \(A^c\)?
#sets
#complement
#squares
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A ({2,3,5,6,7,8})
B ({1,4,9})
C ({2,4,6,8})
D ({1,2,3,4,9})
Explanation opens after your attempt
Correct Answer
A. ({2,3,5,6,7,8})
Step 1
Concept
(A) contains the square numbers (1,4,9) from (U). The complement contains the remaining elements.
Step 2
Why this answer is correct
The correct answer is A. ({2,3,5,6,7,8}). (A) contains the square numbers (1,4,9) from (U). The complement contains the remaining elements.
Step 3
Exam Tip
(A) में (U) के वर्ग संख्याएं (1,4,9) हैं। पूरक में बाकी तत्व आते हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10,11,12\}\) और \(A=\{4,8,12\}\) है, तो \(A^c\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9,10,11,12\}\) and \(A=\{4,8,12\}\), what is \(A^c\)?
#sets
#complement
#multiples
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A ({1,2,3,5,6,7,9,10,11})
B ({4,8,12})
C ({2,4,6,8,10,12})
D ({1,3,5,7,9,11})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,5,6,7,9,10,11})
Step 1
Concept
(A) contains multiples of (4), so the remaining elements of (U) are in \(A^c\). Always answer only within the boundary of (U).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,5,6,7,9,10,11}). (A) contains multiples of (4), so the remaining elements of (U) are in \(A^c\). Always answer only within the boundary of (U).
Step 3
Exam Tip
(A) में (4) के गुणज हैं, इसलिए (U) के बाकी तत्व \(A^c\) में होंगे। हमेशा (U) की सीमा तक ही उत्तर दें।
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यदि \(U=\{0,1,2,3,4,5,6\}\) और \(A=\{0,3,6\}\) है, तो \(A^c\) क्या होगा?
If \(U=\{0,1,2,3,4,5,6\}\) and \(A=\{0,3,6\}\), what is \(A^c\)?
#sets
#complement
#zero
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A ({1,2,4,5})
B ({0,3,6})
C ({1,3,5})
D ({2,4,6})
Explanation opens after your attempt
Correct Answer
A. ({1,2,4,5})
Step 1
Concept
After removing (0,3,6), the elements (1,2,4,5) remain. Treat (0) as a valid element of the set.
Step 2
Why this answer is correct
The correct answer is A. ({1,2,4,5}). After removing (0,3,6), the elements (1,2,4,5) remain. Treat (0) as a valid element of the set.
Step 3
Exam Tip
(0,3,6) हटाने पर (1,2,4,5) बचते हैं। (0) को भी समुच्चय का वैध तत्व मानें।
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\(यदि (U={x:x\in\mathbb{N},1\le x\le 10}) और (A={x:x\) सम है\(}) है, तो (A^c) क्या होगा\)?
\(If (U={x:x\in\mathbb{N},1\le x\le 10}) and (A={x:x\) is even\(}), what is (A^c)\)?
#sets
#complement
#set_builder
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A ({1,3,5,7,9})
B ({2,4,6,8,10})
C ({1,2,3,4,5})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,7,9})
Step 1
Concept
In the given (U), odd numbers remain outside the even numbers. First convert set-builder form into roster form.
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,7,9}). In the given (U), odd numbers remain outside the even numbers. First convert set-builder form into roster form.
Step 3
Exam Tip
दिए गए (U) में सम संख्याओं के बाहर विषम संख्याएं बचती हैं। सेट-बिल्डर रूप को पहले सूची रूप में बदलें।
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यदि \(U={x:x\in\mathbb{N},x<7}\) और \(A={x:x\le 3}\) है, तो \(A^c\) क्या होगा?
If \(U={x:x\in\mathbb{N},x<7}\) and \(A={x:x\le 3}\), what is \(A^c\)?
#sets
#complement
#inequality
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A ({4,5,6})
B ({1,2,3})
C ({3,4,5,6})
D ({1,2,3,4,5,6})
Explanation opens after your attempt
Correct Answer
A. ({4,5,6})
Step 1
Concept
\(U=\{1,2,3,4,5,6\}\) and \(A=\{1,2,3\}\). So the complement is ({4,5,6}).
Step 2
Why this answer is correct
The correct answer is A. ({4,5,6}). \(U=\{1,2,3,4,5,6\}\) and \(A=\{1,2,3\}\). So the complement is ({4,5,6}).
Step 3
Exam Tip
\(U=\{1,2,3,4,5,6\}\) और \(A=\{1,2,3\}\) है। इसलिए पूरक ({4,5,6}) होगा।
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यदि \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,2,5\}\) और \(B=\{2,4,6\}\) है, तो (\(A\cup B\)^c) क्या होगा?
If \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,2,5\}\), and \(B=\{2,4,6\}\), what is (\(A\cup B\)^c)?
#sets
#complement
#union_application
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A ({3,7})
B ({1,2,4,5,6})
C ({2})
D ({1,5,6,7})
Explanation opens after your attempt
Correct Answer
A. ({3,7})
Step 1
Concept
First \(A\cup B={1,2,4,5,6}\). Outside this in (U), (3) and (7) remain.
Step 2
Why this answer is correct
The correct answer is A. ({3,7}). First \(A\cup B={1,2,4,5,6}\). Outside this in (U), (3) and (7) remain.
Step 3
Exam Tip
पहले \(A\cup B={1,2,4,5,6}\) बनता है। (U) में इससे बाहर (3) और (7) बचे हैं।
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यदि \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,2,3,4\}\) और \(B=\{3,4,5\}\) है, तो (\(A\cap B\)^c) क्या होगा?
If \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,2,3,4\}\), and \(B=\{3,4,5\}\), what is (\(A\cap B\)^c)?
#sets
#complement
#intersection_application
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A ({1,2,5,6,7})
B ({3,4})
C ({1,2,3,4,5})
D ({6,7})
Explanation opens after your attempt
Correct Answer
A. ({1,2,5,6,7})
Step 1
Concept
\(A\cap B={3,4}\). Removing (3,4) from (U) gives ({1,2,5,6,7}).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,5,6,7}). \(A\cap B={3,4}\). Removing (3,4) from (U) gives ({1,2,5,6,7}).
Step 3
Exam Tip
\(A\cap B={3,4}\) है। (U) से (3,4) हटाने पर ({1,2,5,6,7}) मिलता है।
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यदि \(A\subseteq B\) है, तो निम्न में से कौन सा संबंध सही है?
If \(A\subseteq B\), which relation is correct?
#sets
#complement
#subset_property
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A \(B^c\subseteq A^c\)
B \(A^c\subseteq B^c\)
C \(A^c=B\)
D \(A^c\cap B^c=U\)
Explanation opens after your attempt
Correct Answer
A. \(B^c\subseteq A^c\)
Step 1
Concept
The order reverses when complements are taken. Thus \(A\subseteq B\) gives \(B^c\subseteq A^c\).
Step 2
Why this answer is correct
The correct answer is A. \(B^c\subseteq A^c\). The order reverses when complements are taken. Thus \(A\subseteq B\) gives \(B^c\subseteq A^c\).
Step 3
Exam Tip
उपसमुच्चय लेने पर पूरक में क्रम उलट जाता है। इसलिए \(A\subseteq B\) से \(B^c\subseteq A^c\) मिलता है।
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कौन सा कथन हर समुच्चय (A) के लिए सही है?
Which statement is true for every set (A)?
#sets
#complement
#double_complement
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A (\(A^c\)^c=A)
B \(A^c=A\)
C \(A\cap A^c=U\)
D \(A\cup A^c=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. (\(A^c\)^c=A)
Step 1
Concept
The complement of the complement is the original set. Hence (\(A^c\)^c=A) is always true.
Step 2
Why this answer is correct
The correct answer is A. (\(A^c\)^c=A). The complement of the complement is the original set. Hence (\(A^c\)^c=A) is always true.
Step 3
Exam Tip
पूरक का पूरक मूल समुच्चय होता है। इसलिए (\(A^c\)^c=A) हमेशा सही है।
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वेन आरेख में \(A^c\) किस भाग को दर्शाता है?
In a Venn diagram, which region represents \(A^c\)?
#sets
#complement
#venn
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A (U) के अंदर (A) के बाहर का भाग / the region inside (U) but outside (A)
B (A) के अंदर का भाग / the region inside (A)
C (U) के बाहर का भाग / the region outside (U)
D \(A\cap U\) का भाग / the region \(A\cap U\)
Explanation opens after your attempt
Correct Answer
A. (U) के अंदर (A) के बाहर का भाग / the region inside (U) but outside (A)
Step 1
Concept
\(A^c\) is always inside (U) but outside (A). In a Venn diagram, do not count the region outside the rectangle.
Step 2
Why this answer is correct
The correct answer is A. (U) के अंदर (A) के बाहर का भाग / the region inside (U) but outside (A). \(A^c\) is always inside (U) but outside (A). In a Venn diagram, do not count the region outside the rectangle.
Step 3
Exam Tip
\(A^c\) हमेशा (U) के अंदर लेकिन (A) के बाहर होता है। वेन आरेख में आयत से बाहर का भाग न गिनें।
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यदि (U) किसी विद्यालय के सभी विद्यार्थी हैं और (A) बस से आने वाले विद्यार्थी हैं, तो \(A^c\) क्या दर्शाता है?
If (U) is the set of all students of a school and (A) is the set of students who come by bus, what does \(A^c\) represent?
#sets
#complement
#application
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A बस से न आने वाले विद्यार्थी / students who do not come by bus
B बस से आने वाले विद्यार्थी / students who come by bus
C सभी विद्यार्थी / all students
D कोई विद्यार्थी नहीं / no student
Explanation opens after your attempt
Correct Answer
A. बस से न आने वाले विद्यार्थी / students who do not come by bus
Step 1
Concept
\(A^c\) contains the students of (U) who are not in (A). So it is the set of students who do not come by bus.
Step 2
Why this answer is correct
The correct answer is A. बस से न आने वाले विद्यार्थी / students who do not come by bus. \(A^c\) contains the students of (U) who are not in (A). So it is the set of students who do not come by bus.
Step 3
Exam Tip
\(A^c\) में (U) के वे विद्यार्थी आएंगे जो (A) में नहीं हैं। इसलिए यह बस से न आने वालों का समुच्चय है।
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\(यदि (U={\)लाल,नीला,हरा,पीला\(}) और (A={\)लाल,पीला\(}) है, तो (A^c) क्या होगा\)?
\(If (U={\)red,blue,green,yellow\(}) and (A={\)red,yellow\(}), what is (A^c)\)?
#sets
#complement
#colors
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A ({नीला,हरा}) / ({blue,green})
B ({लाल,पीला}) / ({red,yellow})
C ({लाल,नीला}) / ({red,blue})
D (U)
Explanation opens after your attempt
Correct Answer
A. ({नीला,हरा}) / ({blue,green})
Step 1
Concept
After removing the colors of (A), blue and green remain. The same rule applies to word sets.
Step 2
Why this answer is correct
The correct answer is A. ({नीला,हरा}) / ({blue,green}). After removing the colors of (A), blue and green remain. The same rule applies to word sets.
Step 3
Exam Tip
(A) के रंग हटाने पर (नीला) और (हरा) बचते हैं। शब्दों वाले समुच्चय में भी वही नियम लगता है।
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\(यदि (U={x:x\) एक अंक है\(}) और (A={0,2,4,6,8}) है, तो (A^c) क्या होगा\)?
\(If (U={x:x\) is a digit\(}) and (A={0,2,4,6,8}), what is (A^c)\)?
#sets
#complement
#digits
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A ({1,3,5,7,9})
B ({0,2,4,6,8})
C ({1,2,3,4,5})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,7,9})
Step 1
Concept
(U) contains all digits and (A) contains even digits. Therefore \(A^c\) contains odd digits.
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,7,9}). (U) contains all digits and (A) contains even digits. Therefore \(A^c\) contains odd digits.
Step 3
Exam Tip
(U) में सभी अंक हैं और (A) में सम अंक हैं। इसलिए \(A^c\) में विषम अंक होंगे।
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यदि (n(U)=48) और (n\(A^c\)=19) है, तो (n(A)) कितना होगा?
If (n(U)=48) and (n\(A^c\)=19), what is (n(A))?
#sets
#complement
#count_reverse
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A (29)
B (67)
C (19)
D (48)
Explanation opens after your attempt
Step 1
Concept
(n(A)=n(U)-n\(A^c\)). Therefore (48-19=29).
Step 2
Why this answer is correct
The correct answer is A. (29). (n(A)=n(U)-n\(A^c\)). Therefore (48-19=29).
Step 3
Exam Tip
(n(A)=n(U)-n\(A^c\)) होता है। इसलिए (48-19=29) मिलेगा।
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यदि (n(U)=24) और (n(A)=n\(A^c\)) है, तो (n(A)) कितना होगा?
If (n(U)=24) and (n(A)=n\(A^c\)), what is (n(A))?
#sets
#complement
#equal_size
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A (12)
B (24)
C (6)
D (0)
Explanation opens after your attempt
Step 1
Concept
(A) and \(A^c\) together form (U), and both have equal size. Hence \(24\div 2=12\).
Step 2
Why this answer is correct
The correct answer is A. (12). (A) and \(A^c\) together form (U), and both have equal size. Hence \(24\div 2=12\).
Step 3
Exam Tip
(A) और \(A^c\) मिलकर (U) बनाते हैं और दोनों बराबर हैं। इसलिए \(24\div 2=12\) होगा।
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यदि (n(U)=31) है, तो (n\(A\cup A^c\)) कितना होगा?
If (n(U)=31), what is (n\(A\cup A^c\))?
#sets
#complement
#union_count
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A (31)
B (0)
C (n(A))
D (n\(A^c\))
Explanation opens after your attempt
Step 1
Concept
\(A\cup A^c=U\). Therefore (n\(A\cup A^c\)=31).
Step 2
Why this answer is correct
The correct answer is A. (31). \(A\cup A^c=U\). Therefore (n\(A\cup A^c\)=31).
Step 3
Exam Tip
\(A\cup A^c=U\) होता है। इसलिए (n\(A\cup A^c\)=31) होगा।
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यदि \(U=\{2,4,6,8,10,12\}\) और \(A=\{4,8,12\}\) है, तो (U-A) क्या होगा?
If \(U=\{2,4,6,8,10,12\}\) and \(A=\{4,8,12\}\), what is (U-A)?
#sets
#complement
#set_difference
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A ({2,6,10})
B ({4,8,12})
C ({2,4,6})
D (U)
Explanation opens after your attempt
Correct Answer
A. ({2,6,10})
Step 1
Concept
(U-A) is the same as \(A^c\). Removing (4,8,12) leaves (2,6,10).
Step 2
Why this answer is correct
The correct answer is A. ({2,6,10}). (U-A) is the same as \(A^c\). Removing (4,8,12) leaves (2,6,10).
Step 3
Exam Tip
(U-A) वही है जो \(A^c\) है। (4,8,12) हटाने पर (2,6,10) बचते हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\) और \(A^c={2,4,6,8}\) है, तो \(A\cap A^c\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A^c={2,4,6,8}\), what is \(A\cap A^c\)?
#sets
#complement
#shortcut
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A \(\varnothing\) / empty set
B ({2,4,6,8})
C ({1,3,5,7})
D (U)
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\) / empty set
Step 1
Concept
(A) and \(A^c\) have no common element. Therefore \(A\cap A^c=\varnothing\) directly.
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\) / empty set. (A) and \(A^c\) have no common element. Therefore \(A\cap A^c=\varnothing\) directly.
Step 3
Exam Tip
(A) और \(A^c\) में कोई साझा तत्व नहीं होता। इसलिए \(A\cap A^c=\varnothing\) सीधे मिलता है।
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यदि \(U=\{a,b,c,d,e\}\) और \(A^c={b,e}\) है, तो \(A\cup A^c\) क्या होगा?
If \(U=\{a,b,c,d,e\}\) and \(A^c={b,e}\), what is \(A\cup A^c\)?
#sets
#complement
#union_shortcut
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A (U)
B ({b,e})
C \(\varnothing\)
D ({a,c,d})
Explanation opens after your attempt
Step 1
Concept
\(A\cup A^c\) is always the whole (U). So it is not necessary to find (A).
Step 2
Why this answer is correct
The correct answer is A. (U). \(A\cup A^c\) is always the whole (U). So it is not necessary to find (A).
Step 3
Exam Tip
\(A\cup A^c\) हमेशा पूरा (U) होता है। इसलिए (A) निकालना जरूरी नहीं है।
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यदि \(6\in U\) और \(6\notin A\) है, तो सही निष्कर्ष कौन सा है?
If \(6\in U\) and \(6\notin A\), which conclusion is correct?
#sets
#complement
#element_logic
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A \(6\in A^c\)
B \(6\in A\)
C \(6\notin U\)
D \(6\in A\cap A^c\)
Explanation opens after your attempt
Correct Answer
A. \(6\in A^c\)
Step 1
Concept
An element that is in (U) but not in (A) belongs to \(A^c\). This is the membership condition of complement.
Step 2
Why this answer is correct
The correct answer is A. \(6\in A^c\). An element that is in (U) but not in (A) belongs to \(A^c\). This is the membership condition of complement.
Step 3
Exam Tip
जो तत्व (U) में है लेकिन (A) में नहीं है, वह \(A^c\) में होगा। यही पूरक की सदस्यता शर्त है।
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यदि \(5\notin A^c\) और \(5\in U\) है, तो कौन सा कथन सही है?
If \(5\notin A^c\) and \(5\in U\), which statement is correct?
#sets
#complement
#reasoning
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A \(5\in A\)
B \(5\notin U\)
C \(5\in A^c\)
D \(5\in A\cap A^c\)
Explanation opens after your attempt
Correct Answer
A. \(5\in A\)
Step 1
Concept
An element of (U) belongs either to (A) or to \(A^c\). If it is not in \(A^c\), then it is in (A).
Step 2
Why this answer is correct
The correct answer is A. \(5\in A\). An element of (U) belongs either to (A) or to \(A^c\). If it is not in \(A^c\), then it is in (A).
Step 3
Exam Tip
(U) का कोई तत्व या तो (A) में होगा या \(A^c\) में। यदि वह \(A^c\) में नहीं है, तो वह (A) में होगा।
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यदि (U=[1,9]) और (A=[1,5)) है, तो \(A^c\) क्या होगा?
If (U=[1,9]) and (A=[1,5)), what is \(A^c\)?
#sets
#complement
#intervals
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A ([5,9])
B ((5,9])
C ([1,5))
D ([1,9])
Explanation opens after your attempt
Correct Answer
A. ([5,9])
Step 1
Concept
(5) is not included in (A), so (5) comes in the complement. Since (9) is included in (U), ([5,9]) is correct.
Step 2
Why this answer is correct
The correct answer is A. ([5,9]). (5) is not included in (A), so (5) comes in the complement. Since (9) is included in (U), ([5,9]) is correct.
Step 3
Exam Tip
(5) (A) में शामिल नहीं है, इसलिए (5) पूरक में आएगा। (9) (U) में शामिल है, इसलिए ([5,9]) सही है।
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यदि (U=(-3,4]) और (A=(-3,1]) है, तो \(A^c\) क्या होगा?
If (U=(-3,4]) and (A=(-3,1]), what is \(A^c\)?
#sets
#complement
#interval_reasoning
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A ( (1,4] )
B ( [1,4] )
C ( (-3,1] )
D ( (-3,4] )
Explanation opens after your attempt
Correct Answer
A. ( (1,4] )
Step 1
Concept
(1) is included in (A), so the complement starts after (1). (4) is included in (U).
Step 2
Why this answer is correct
The correct answer is A. ( (1,4] ). (1) is included in (A), so the complement starts after (1). (4) is included in (U).
Step 3
Exam Tip
(1) (A) में शामिल है, इसलिए पूरक (1) के बाद से शुरू होगा। (4) (U) में शामिल है।
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यदि \(U={x:x\in\mathbb{Z},-2\le x\le 3}\) और \(A=\{-1,0,1\}\) है, तो \(A^c\) क्या होगा?
If \(U={x:x\in\mathbb{Z},-2\le x\le 3}\) and \(A=\{-1,0,1\}\), what is \(A^c\)?
#sets
#complement
#integers
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A ({-2,2,3})
B ({-1,0,1})
C ({-2,-1,0})
D ({1,2,3})
Explanation opens after your attempt
Correct Answer
A. ({-2,2,3})
Step 1
Concept
\(U=\{-2,-1,0,1,2,3\}\). Removing (-1,0,1) leaves (-2,2,3).
Step 2
Why this answer is correct
The correct answer is A. ({-2,2,3}). \(U=\{-2,-1,0,1,2,3\}\). Removing (-1,0,1) leaves (-2,2,3).
Step 3
Exam Tip
\(U=\{-2,-1,0,1,2,3\}\) है। इसमें से (-1,0,1) हटाने पर (-2,2,3) बचते हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\) और \(A=\{2,3,5,7\}\) है, तो कौन सा तत्व \(A^c\) में है?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A=\{2,3,5,7\}\), which element is in \(A^c\)?
#sets
#complement
#element_selection
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A (9)
B (2)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(9\in U\) and \(9\notin A\), so \(9\in A^c\). Choose the option that is not in (A).
Step 2
Why this answer is correct
The correct answer is A. (9). \(9\in U\) and \(9\notin A\), so \(9\in A^c\). Choose the option that is not in (A).
Step 3
Exam Tip
\(9\in U\) है और \(9\notin A\), इसलिए \(9\in A^c\)। विकल्पों में वही तत्व चुनें जो (A) में न हो।
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यदि \(U=\{1,2,3,4,5\}\) और \(A=\{2,5\}\) है, तो कौन सा कथन सही है?
If \(U=\{1,2,3,4,5\}\) and \(A=\{2,5\}\), which statement is correct?
#sets
#complement
#true_statement
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A \(4\in A^c\)
B \(2\in A^c\)
C \(5\notin A\)
D \(1\in A\)
Explanation opens after your attempt
Correct Answer
A. \(4\in A^c\)
Step 1
Concept
\(A^c={1,3,4}\), so \(4\in A^c\) is correct. Writing the complement first reduces confusion.
Step 2
Why this answer is correct
The correct answer is A. \(4\in A^c\). \(A^c={1,3,4}\), so \(4\in A^c\) is correct. Writing the complement first reduces confusion.
Step 3
Exam Tip
\(A^c={1,3,4}\), इसलिए \(4\in A^c\) सही है। पहले पूरक लिखने से भ्रम कम होता है।
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\(यदि (U={x:x\) भारत के चार प्रमुख दिशाएं हैं\(}) और (A={\)उत्तर,दक्षिण\(}) है, तो (A^c) क्या होगा\)?
\(If (U={x:x\) is one of the four main directions\(}) and (A={\)north,south\(}), what is (A^c)\)?
#sets
#complement
#word_set
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A ({पूर्व,पश्चिम}) / ({east,west})
B ({उत्तर,दक्षिण}) / ({north,south})
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({पूर्व,पश्चिम}) / ({east,west})
Step 1
Concept
Among the four directions, removing north and south leaves east and west. Complement depends on the reference set.
Step 2
Why this answer is correct
The correct answer is A. ({पूर्व,पश्चिम}) / ({east,west}). Among the four directions, removing north and south leaves east and west. Complement depends on the reference set.
Step 3
Exam Tip
चार दिशाओं में (उत्तर) और (दक्षिण) हटाने पर (पूर्व) और (पश्चिम) बचते हैं। पूरक संदर्भ समुच्चय पर निर्भर करता है।
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यदि (U) में (60) विद्यार्थी हैं और (A) में (18) विद्यार्थी संगीत सीखते हैं, तो संगीत न सीखने वाले विद्यार्थियों की संख्या क्या है?
If (U) has (60) students and (A) has (18) students learning music, what is the number of students not learning music?
#sets
#complement
#word_problem
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A (42)
B (78)
C (18)
D (60)
Explanation opens after your attempt
Step 1
Concept
Students not learning music are in \(A^c\). Therefore the number is (60-18=42).
Step 2
Why this answer is correct
The correct answer is A. (42). Students not learning music are in \(A^c\). Therefore the number is (60-18=42).
Step 3
Exam Tip
संगीत न सीखने वाले \(A^c\) में हैं। इसलिए संख्या (60-18=42) है।
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यदि किसी कक्षा में (n(U)=45) और (n(A)=28) है, तो (n\(A^c\)) का अर्थ क्या है?
If in a class (n(U)=45) and (n(A)=28), what does (n\(A^c\)) mean?
#sets
#complement
#meaning
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A (A) में न आने वाले विद्यार्थियों की संख्या / number of students not in (A)
B (A) में आने वाले विद्यार्थियों की संख्या / number of students in (A)
C कुल विद्यार्थियों की संख्या / total number of students
D साझा विद्यार्थियों की संख्या / number of common students
Explanation opens after your attempt
Correct Answer
A. (A) में न आने वाले विद्यार्थियों की संख्या / number of students not in (A)
Step 1
Concept
(n\(A^c\)) is the number of elements in (U) but not in (A). Its value here is (45-28=17).
Step 2
Why this answer is correct
The correct answer is A. (A) में न आने वाले विद्यार्थियों की संख्या / number of students not in (A). (n\(A^c\)) is the number of elements in (U) but not in (A). Its value here is (45-28=17).
Step 3
Exam Tip
(n\(A^c\)) उन तत्वों की संख्या है जो (U) में हैं पर (A) में नहीं हैं। इसका मान यहां (45-28=17) होगा।
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यदि (A) सार्वत्रिक समुच्चय (U) का वास्तविक उपसमुच्चय है, तो कौन सा कथन सही है?
If (A) is a proper subset of the universal set (U), which statement is correct?
#sets
#complement
#proper_subset
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A \(A^c\ne\varnothing\)
B \(A^c=\varnothing\)
C \(A^c=A\)
D \(A^c\not\subseteq U\)
Explanation opens after your attempt
Correct Answer
A. \(A^c\ne\varnothing\)
Step 1
Concept
In a proper subset, at least one element of (U) is outside (A). Therefore \(A^c\) will not be empty.
Step 2
Why this answer is correct
The correct answer is A. \(A^c\ne\varnothing\). In a proper subset, at least one element of (U) is outside (A). Therefore \(A^c\) will not be empty.
Step 3
Exam Tip
वास्तविक उपसमुच्चय में (U) का कम से कम एक तत्व (A) से बाहर होता है। इसलिए \(A^c\) खाली नहीं होगा।
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यदि \(A=\{2,4\}\), \(U_1={1,2,3,4}\) और \(U_2={1,2,3,4,5}\) हैं, तो \(A^c\) अलग क्यों हो सकता है?
If \(A=\{2,4\}\), \(U_1={1,2,3,4}\), and \(U_2={1,2,3,4,5}\), why can \(A^c\) be different?
#sets
#complement
#universal_dependency
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A क्योंकि सार्वत्रिक समुच्चय बदल गया है / because the universal set has changed
B क्योंकि (A) बदल गया है / because (A) has changed
C क्योंकि \(2\in A\) है / because \(2\in A\)
D क्योंकि \(4\in A\) है / because \(4\in A\)
Explanation opens after your attempt
Correct Answer
A. क्योंकि सार्वत्रिक समुच्चय बदल गया है / because the universal set has changed
Step 1
Concept
Complement always depends on the chosen (U). When (U) changes, \(A^c\) may also change.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि सार्वत्रिक समुच्चय बदल गया है / because the universal set has changed. Complement always depends on the chosen (U). When (U) changes, \(A^c\) may also change.
Step 3
Exam Tip
पूरक हमेशा चुने गए (U) पर निर्भर करता है। (U) बदलने पर \(A^c\) भी बदल सकता है।
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किसी दिए गए (B) को (A) का पूरक जांचने के लिए सबसे अच्छा परीक्षण कौन सा है?
What is the best test to check whether a given (B) is the complement of (A)?
#sets
#complement
#property_check
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A \(A\cap B=\varnothing\) और \(A\cup B=U\) / \(A\cap B=\varnothing\) and \(A\cup B=U\)
B \(A\cap B=U\) और \(A\cup B=\varnothing\) / \(A\cap B=U\) and \(A\cup B=\varnothing\)
C (A=B) और (B=U) / (A=B) and (B=U)
D \(A\subset B\) और \(B\subset A\) / \(A\subset B\) and \(B\subset A\)
Explanation opens after your attempt
Correct Answer
A. \(A\cap B=\varnothing\) और \(A\cup B=U\) / \(A\cap B=\varnothing\) and \(A\cup B=U\)
Step 1
Concept
For (B) to be the complement of (A), they must have no common element and together form (U). This is the safest exam check.
Step 2
Why this answer is correct
The correct answer is A. \(A\cap B=\varnothing\) और \(A\cup B=U\) / \(A\cap B=\varnothing\) and \(A\cup B=U\). For (B) to be the complement of (A), they must have no common element and together form (U). This is the safest exam check.
Step 3
Exam Tip
पूरक होने के लिए (A) और (B) में कोई साझा तत्व नहीं होना चाहिए और दोनों मिलकर (U) बनाने चाहिए। यही परीक्षा में सबसे सुरक्षित जांच है।
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यदि \(U=\{10,11,12,13,14,15\}\) और \(A=\{11,13,15\}\) है, तो \(A^c\) क्या होगा?
If \(U=\{10,11,12,13,14,15\}\) and \(A=\{11,13,15\}\), what will \(A^c\) be?
#sets
#complement
#finite_sets
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A ({10,12,14})
B ({11,13,15})
C ({10,11,12})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({10,12,14})
Step 1
Concept
\(A^c\) contains the elements of (U) that are not in (A). So after removing (11,13,15), (10,12,14) remain.
Step 2
Why this answer is correct
The correct answer is A. ({10,12,14}). \(A^c\) contains the elements of (U) that are not in (A). So after removing (11,13,15), (10,12,14) remain.
Step 3
Exam Tip
\(A^c\) में (U) के वे तत्व आते हैं जो (A) में नहीं हैं। इसलिए (11,13,15) हटाने पर (10,12,14) बचते हैं।
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\(यदि (U={x:x\in\mathbb{N},1\le x\le 15}) और (A={x:x\) 5 का गुणज है\(}) है, तो (A^c) क्या होगा\)?
\(If (U={x:x\in\mathbb{N},1\le x\le 15}) and (A={x:x\) is a multiple of \(5}), what will (A^c) be\)?
#sets
#complement
#multiples
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A ({1,2,3,4,6,7,8,9,11,12,13,14})
B ({5,10,15})
C ({1,5,10,15})
D ({2,4,6,8,10,12,14})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4,6,7,8,9,11,12,13,14})
Step 1
Concept
\(A=\{5,10,15\}\). Removing these from (U) gives the remaining elements of \(A^c\).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4,6,7,8,9,11,12,13,14}). \(A=\{5,10,15\}\). Removing these from (U) gives the remaining elements of \(A^c\).
Step 3
Exam Tip
\(A=\{5,10,15\}\) है। (U) से इन्हें हटाने पर बाकी तत्व \(A^c\) बनाते हैं।
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यदि \(U=\{a,e,i,o,u,b,c,d\}\) और \(A=\{a,e,i,o,u\}\) है, तो \(A^c\) क्या है?
If \(U=\{a,e,i,o,u,b,c,d\}\) and \(A=\{a,e,i,o,u\}\), what is \(A^c\)?
#sets
#complement
#letters
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A ({b,c,d})
B ({a,e,i,o,u})
C ({a,b,c})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({b,c,d})
Step 1
Concept
(A) contains vowels, so the remaining elements (b,c,d) of (U) are in the complement. Complement is always found with respect to (U).
Step 2
Why this answer is correct
The correct answer is A. ({b,c,d}). (A) contains vowels, so the remaining elements (b,c,d) of (U) are in the complement. Complement is always found with respect to (U).
Step 3
Exam Tip
(A) में स्वर हैं, इसलिए (U) में बचे (b,c,d) पूरक में होंगे। पूरक हमेशा (U) के आधार पर निकाला जाता है।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,7\}\) और \(B=\{2,3,8\}\) है, तो (\(A\cup B\)^c) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,7\}\), and \(B=\{2,3,8\}\), what will (\(A\cup B\)^c) be?
#sets
#complement
#union_application
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A ({4,5,6})
B ({1,2,3,7,8})
C ({2})
D ({4,5,6,7})
Explanation opens after your attempt
Correct Answer
A. ({4,5,6})
Step 1
Concept
First \(A\cup B={1,2,3,7,8}\). Outside this in (U), (4,5,6) remain.
Step 2
Why this answer is correct
The correct answer is A. ({4,5,6}). First \(A\cup B={1,2,3,7,8}\). Outside this in (U), (4,5,6) remain.
Step 3
Exam Tip
पहले \(A\cup B={1,2,3,7,8}\) है। (U) में इससे बाहर (4,5,6) बचे हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{2,4,6,8\}\) और \(B=\{3,6,9\}\) है, तो (\(A\cap B\)^c) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{2,4,6,8\}\), and \(B=\{3,6,9\}\), what will (\(A\cap B\)^c) be?
#sets
#complement
#intersection_application
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A ({1,2,3,4,5,7,8,9})
B ({6})
C ({2,3,4,6,8,9})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4,5,7,8,9})
Step 1
Concept
Here \(A\cap B={6}\). So removing (6) from (U) gives (\(A\cap B\)^c).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4,5,7,8,9}). Here \(A\cap B={6}\). So removing (6) from (U) gives (\(A\cap B\)^c).
Step 3
Exam Tip
यहां \(A\cap B={6}\) है। इसलिए (U) से (6) हटाने पर (\(A\cap B\)^c) मिलता है।
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यदि (n(U)=72) और (n\(A^c\)=31) है, तो (n(A)) कितना होगा?
If (n(U)=72) and (n\(A^c\)=31), what is (n(A))?
#sets
#complement
#cardinality
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A (41)
B (103)
C (31)
D (72)
Explanation opens after your attempt
Step 1
Concept
(n(A)=n(U)-n\(A^c\)). Therefore (72-31=41) is correct.
Step 2
Why this answer is correct
The correct answer is A. (41). (n(A)=n(U)-n\(A^c\)). Therefore (72-31=41) is correct.
Step 3
Exam Tip
(n(A)=n(U)-n\(A^c\)) होता है। इसलिए (72-31=41) सही है।
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यदि (U=[0,12]) और (A=(3,8]) है, तो \(A^c\) क्या होगा?
If (U=[0,12]) and (A=(3,8]), what will \(A^c\) be?
#sets
#complement
#intervals
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A ([0,3]\cup(8,12])
B ([0,3)\cup[8,12])
C ((3,8])
D ([0,12])
Explanation opens after your attempt
Correct Answer
A. ([0,3]\cup(8,12])
Step 1
Concept
(3) is not included in (A), so it comes in the complement. (8) is in (A), so the complement starts after (8).
Step 2
Why this answer is correct
The correct answer is A. ([0,3]\cup(8,12]). (3) is not included in (A), so it comes in the complement. (8) is in (A), so the complement starts after (8).
Step 3
Exam Tip
(3) (A) में शामिल नहीं है, इसलिए वह पूरक में आएगा। (8) (A) में है, इसलिए पूरक (8) के बाद से शुरू होगा।
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यदि \(U={x:x\in\mathbb{Z},-3\le x\le 4}\) और \(A=\{-2,0,2,4\}\) है, तो \(A^c\) क्या होगा?
If \(U={x:x\in\mathbb{Z},-3\le x\le 4}\) and \(A=\{-2,0,2,4\}\), what will \(A^c\) be?
#sets
#complement
#integers
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A ({-3,-1,1,3})
B ({-2,0,2,4})
C ({-3,-2,-1,0})
D ({1,2,3,4})
Explanation opens after your attempt
Correct Answer
A. ({-3,-1,1,3})
Step 1
Concept
\(U=\{-3,-2,-1,0,1,2,3,4\}\). Removing the elements of (A) leaves (-3,-1,1,3).
Step 2
Why this answer is correct
The correct answer is A. ({-3,-1,1,3}). \(U=\{-3,-2,-1,0,1,2,3,4\}\). Removing the elements of (A) leaves (-3,-1,1,3).
Step 3
Exam Tip
\(U=\{-3,-2,-1,0,1,2,3,4\}\) है। इसमें से (A) के तत्व हटाने पर (-3,-1,1,3) बचते हैं।
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यदि किसी कक्षा में (n(U)=55) विद्यार्थी हैं और (n(A)=37) विद्यार्थी गणित पसंद करते हैं, तो गणित पसंद न करने वाले विद्यार्थियों की संख्या क्या है?
If a class has (n(U)=55) students and (n(A)=37) students like mathematics, what is the number of students who do not like mathematics?
#sets
#complement
#word_problem
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A (18)
B (92)
C (37)
D (55)
Explanation opens after your attempt
Step 1
Concept
Students who do not like mathematics are in \(A^c\). Therefore the number is (55-37=18).
Step 2
Why this answer is correct
The correct answer is A. (18). Students who do not like mathematics are in \(A^c\). Therefore the number is (55-37=18).
Step 3
Exam Tip
गणित पसंद न करने वाले विद्यार्थी \(A^c\) में हैं। इसलिए संख्या (55-37=18) होगी।
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यदि (B) को (A) का पूरक कहा गया है, तो कौन सा कथन अवश्य सही होगा?
If (B) is called the complement of (A), which statement must be true?
#sets
#complement
#property_check
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A \(A\cap B=\varnothing\) और \(A\cup B=U\) / \(A\cap B=\varnothing\) and \(A\cup B=U\)
B \(A\cap B=U\) और \(A\cup B=\varnothing\) / \(A\cap B=U\) and \(A\cup B=\varnothing\)
C (A=B)
D \(B\not\subseteq U\)
Explanation opens after your attempt
Correct Answer
A. \(A\cap B=\varnothing\) और \(A\cup B=U\) / \(A\cap B=\varnothing\) and \(A\cup B=U\)
Step 1
Concept
A complement set is disjoint from (A), and together they form (U). This is the simplest rule to check complement.
Step 2
Why this answer is correct
The correct answer is A. \(A\cap B=\varnothing\) और \(A\cup B=U\) / \(A\cap B=\varnothing\) and \(A\cup B=U\). A complement set is disjoint from (A), and together they form (U). This is the simplest rule to check complement.
Step 3
Exam Tip
पूरक समुच्चय (A) से असंबद्ध होता है और दोनों मिलकर (U) बनाते हैं। यही पूरक जांचने का सबसे सरल नियम है।
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