यदि \(A=\{4,6,8\}\) है तो (\mathcal{P}(A)) में कितने तत्व होंगे?
If \(A=\{4,6,8\}\) then how many elements will be in (\mathcal{P}(A))?
#sets
#power_set
#cardinality
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A (3)
B (6)
C (8)
D (12)
Explanation opens after your attempt
Step 1
Concept
Set (A) has (3) elements so its power set has \(2^3=8\) elements. Use the \(2^n\) rule directly in exams.
Step 2
Why this answer is correct
The correct answer is C. (8). Set (A) has (3) elements so its power set has \(2^3=8\) elements. Use the \(2^n\) rule directly in exams.
Step 3
Exam Tip
(A) में (3) तत्व हैं इसलिए घात समुच्चय में \(2^3=8\) तत्व होंगे। परीक्षा में \(2^n\) नियम तुरंत लगाएं।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3\}\) और \(B=\{3,4,5\}\) हैं तो (\(A\cup B\)') क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3\}\) and \(B=\{3,4,5\}\), what is (\(A\cup B\)')?
#sets
#power_set
#universal_set
#complement_union
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A ({1,2,3,4,5})
B ({6,7,8})
C ({1,2,6,7,8})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
B. ({6,7,8})
Step 1
Concept
First \(A\cup B={1,2,3,4,5}\). Its complement is the remaining elements ({6,7,8}) in (U).
Step 2
Why this answer is correct
The correct answer is B. ({6,7,8}). First \(A\cup B={1,2,3,4,5}\). Its complement is the remaining elements ({6,7,8}) in (U).
Step 3
Exam Tip
पहले \(A\cup B={1,2,3,4,5}\) है। इसका पूरक (U) में बचे हुए ({6,7,8}) होंगे।
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यदि \(A=\{u,v\}\) है तो इनमें से कौन सा (\mathcal{P}(A)) का तत्व है?
If \(A=\{u,v\}\) then which of the following is an element of (\mathcal{P}(A))?
#sets
#power_set
#subset
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A (u)
B ({v})
C (v)
D (uv)
Explanation opens after your attempt
Step 1
Concept
({v}) is a subset of (A) so it is an element of (\mathcal{P}(A)). A power set contains subsets.
Step 2
Why this answer is correct
The correct answer is B. ({v}). ({v}) is a subset of (A) so it is an element of (\mathcal{P}(A)). A power set contains subsets.
Step 3
Exam Tip
({v}) (A) का उपसमुच्चय है इसलिए यह (\mathcal{P}(A)) का तत्व है। घात समुच्चय में उपसमुच्चय आते हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\) और \(A=\{2,4,8\}\) है तो (A') क्या है?
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{2,4,8\}\), what is (A')?
#sets
#universal_set
#complement
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A ({2,4,8})
B ({1,3,5,6,7})
C ({1,2,3,4})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
B. ({1,3,5,6,7})
Step 1
Concept
The complement contains elements of (U) that are not in (A). Here (1,3,5,6,7) remain.
Step 2
Why this answer is correct
The correct answer is B. ({1,3,5,6,7}). The complement contains elements of (U) that are not in (A). Here (1,3,5,6,7) remain.
Step 3
Exam Tip
पूरक में (U) के वे तत्व आते हैं जो (A) में नहीं हैं। यहां (1,3,5,6,7) बचते हैं।
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यदि (n(\mathcal{P}(A))=64) है तो (n(A)) कितना होगा?
If (n(\mathcal{P}(A))=64), what is (n(A))?
#sets
#power_set
#reverse_count
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A (4)
B (5)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
Since \(64=2^6\), (n(A)=6). Match the power set size with \(2^n\).
Step 2
Why this answer is correct
The correct answer is C. (6). Since \(64=2^6\), (n(A)=6). Match the power set size with \(2^n\).
Step 3
Exam Tip
क्योंकि \(64=2^6\) इसलिए (n(A)=6) है। घात समुच्चय की संख्या को \(2^n\) से मिलाएं।
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यदि \(A=\{9\}\) है तो (\mathcal{P}(A)) कौन सा है?
If \(A=\{9\}\), which is (\mathcal{P}(A))?
#sets
#power_set
#singleton
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A ({9})
B \({\emptyset,9}\)
C \({\emptyset,{9}}\)
D ({{9},9})
Explanation opens after your attempt
Correct Answer
C. \({\emptyset,{9}}\)
Step 1
Concept
A one element set has subsets \(\emptyset\) and ({9}). Hence the power set is \({\emptyset,{9}}\).
Step 2
Why this answer is correct
The correct answer is C. \({\emptyset,{9}}\). A one element set has subsets \(\emptyset\) and ({9}). Hence the power set is \({\emptyset,{9}}\).
Step 3
Exam Tip
एक तत्व वाले समुच्चय के उपसमुच्चय \(\emptyset\) और ({9}) होते हैं। इसलिए घात समुच्चय \({\emptyset,{9}}\) है।
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यदि \(U=\{a,b,c,d,f\}\) और \(C=\{a,c,f\}\) है तो (C') में कौन सा तत्व होगा?
If \(U=\{a,b,c,d,f\}\) and \(C=\{a,c,f\}\), which element will be in (C')?
#sets
#universal_set
#element_check
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A (a)
B (b)
C (c)
D (f)
Explanation opens after your attempt
Step 1
Concept
(b) is in (U) but not in (C). Therefore (b) will be in (C').
Step 2
Why this answer is correct
The correct answer is B. (b). (b) is in (U) but not in (C). Therefore (b) will be in (C').
Step 3
Exam Tip
(b) (U) में है लेकिन (C) में नहीं है। इसलिए (b) (C') में होगा।
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यदि \(A=\{3,6,9\}\) है तो ({3,9}) के लिए सही कथन कौन सा है?
If \(A=\{3,6,9\}\), which statement is correct for ({3,9})?
#sets
#power_set
#element_relation
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A \({3,9}\in A\)
B \({3,9}\in \mathcal{P}(A)\)
C ({3,9}=A)
D \({3,9}\not\subseteq A\)
Explanation opens after your attempt
Correct Answer
B. \({3,9}\in \mathcal{P}(A)\)
Step 1
Concept
({3,9}) is a subset of (A). So it is an element of (\mathcal{P}(A)).
Step 2
Why this answer is correct
The correct answer is B. \({3,9}\in \mathcal{P}(A)\). ({3,9}) is a subset of (A). So it is an element of (\mathcal{P}(A)).
Step 3
Exam Tip
({3,9}) (A) का उपसमुच्चय है। इसलिए यह (\mathcal{P}(A)) का तत्व है।
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यदि \(U=\{0,1,2,3,4,5,6\}\) और \(A=\{1,3,5\}\) है तो (n(A')) कितना है?
If \(U=\{0,1,2,3,4,5,6\}\) and \(A=\{1,3,5\}\), what is (n(A'))?
#sets
#universal_set
#complement_count
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A (3)
B (4)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
(A') contains (0,2,4,6). Therefore (n(A')=4).
Step 2
Why this answer is correct
The correct answer is B. (4). (A') contains (0,2,4,6). Therefore (n(A')=4).
Step 3
Exam Tip
(A') में (0,2,4,6) हैं। इसलिए (n(A')=4) है।
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यदि \(A={\emptyset,5,10}\) है तो (n(\mathcal{P}(A))) कितना होगा?
If \(A={\emptyset,5,10}\), what is (n(\mathcal{P}(A)))?
#sets
#power_set
#empty_element
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A (3)
B (6)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
Here \(\emptyset\) is also one element so (A) has (3) elements. Thus there are \(2^3=8\) subsets.
Step 2
Why this answer is correct
The correct answer is C. (8). Here \(\emptyset\) is also one element so (A) has (3) elements. Thus there are \(2^3=8\) subsets.
Step 3
Exam Tip
यहां \(\emptyset\) भी एक तत्व है इसलिए (A) में कुल (3) तत्व हैं। अतः \(2^3=8\) उपसमुच्चय होंगे।
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यदि (U) पुस्तकालय की सभी पुस्तकों का समुच्चय है और (H) हिंदी पुस्तकों का समुच्चय है तो (H') क्या दर्शाएगा?
If (U) is the set of all books in a library and (H) is the set of Hindi books, what does (H') represent?
#sets
#universal_set
#word_problem
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A हिंदी पुस्तकें / Hindi books
B पुस्तकालय की हिंदी न होने वाली पुस्तकें / library books that are not Hindi books
C सभी लेखक / all authors
D केवल नई पुस्तकें / only new books
Explanation opens after your attempt
Correct Answer
B. पुस्तकालय की हिंदी न होने वाली पुस्तकें / library books that are not Hindi books
Step 1
Concept
A complement shows elements inside the same (U) but outside the given set. Here (H') means books that are not Hindi books.
Step 2
Why this answer is correct
The correct answer is B. पुस्तकालय की हिंदी न होने वाली पुस्तकें / library books that are not Hindi books. A complement shows elements inside the same (U) but outside the given set. Here (H') means books that are not Hindi books.
Step 3
Exam Tip
पूरक उसी (U) के अंदर दिए गए समुच्चय से बाहर के तत्व दिखाता है। यहां (H') हिंदी न होने वाली पुस्तकें हैं।
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यदि \(A=\{l,m,n,o,p\}\) है तो (\mathcal{P}(A)) में कितने एक तत्व वाले उपसमुच्चय होंगे?
If \(A=\{l,m,n,o,p\}\), how many one element subsets are in (\mathcal{P}(A))?
#sets
#power_set
#singleton_subsets
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A (1)
B (5)
C (10)
D (32)
Explanation opens after your attempt
Step 1
Concept
Each element forms one singleton subset. With five elements there are five one element subsets.
Step 2
Why this answer is correct
The correct answer is B. (5). Each element forms one singleton subset. With five elements there are five one element subsets.
Step 3
Exam Tip
हर तत्व से एक एकल उपसमुच्चय बनता है। पांच तत्व होने पर पांच एक तत्व वाले उपसमुच्चय होंगे।
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यदि \(A=\{2,4,6,8\}\) है तो कौन सा (\mathcal{P}(A)) का तत्व नहीं है?
If \(A=\{2,4,6,8\}\), which is not an element of (\mathcal{P}(A))?
#sets
#power_set
#not_subset
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A ({2,8})
B ({4,6})
C \(\emptyset\)
D ({2,10})
Explanation opens after your attempt
Correct Answer
D. ({2,10})
Step 1
Concept
({2,10}) contains (10), which is not in (A). So it is not a subset of (A).
Step 2
Why this answer is correct
The correct answer is D. ({2,10}). ({2,10}) contains (10), which is not in (A). So it is not a subset of (A).
Step 3
Exam Tip
({2,10}) में (10) है जो (A) में नहीं है। इसलिए यह (A) का उपसमुच्चय नहीं है।
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यदि \(A\subseteq U\) है तो \(A'\cap A\) क्या होगा?
If \(A\subseteq U\), what is \(A'\cap A\)?
#sets
#universal_set
#intersection_complement
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A (U)
B (A)
C \(\emptyset\)
D (A')
Explanation opens after your attempt
Correct Answer
C. \(\emptyset\)
Step 1
Concept
No element can be in both (A) and (A') at the same time. Hence the intersection is empty.
Step 2
Why this answer is correct
The correct answer is C. \(\emptyset\). No element can be in both (A) and (A') at the same time. Hence the intersection is empty.
Step 3
Exam Tip
कोई तत्व (A) और (A') दोनों में एक साथ नहीं हो सकता। इसलिए प्रतिच्छेद रिक्त है।
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यदि \(A=\{11,22\}\) है तो (\mathcal{P}(A)) कौन सा है?
If \(A=\{11,22\}\), which is (\mathcal{P}(A))?
#sets
#power_set
#list_subsets
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A \({\emptyset,{11},{22},{11,22}}\)
B ({11,22})
C ({{11},{22}})
D \({\emptyset,11,22}\)
Explanation opens after your attempt
Correct Answer
A. \({\emptyset,{11},{22},{11,22}}\)
Step 1
Concept
A two element set has four subsets. Include \(\emptyset\) and the whole set in the power set.
Step 2
Why this answer is correct
The correct answer is A. \({\emptyset,{11},{22},{11,22}}\). A two element set has four subsets. Include \(\emptyset\) and the whole set in the power set.
Step 3
Exam Tip
दो तत्वों वाले समुच्चय के चार उपसमुच्चय होते हैं। घात समुच्चय में \(\emptyset\) और पूरा समुच्चय भी शामिल करें।
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यदि \(U=\{1,2,3,4,5,6,7,9\}\) और \(A=\{1,3,5,7,9\}\) है तो (A') क्या है?
If \(U=\{1,2,3,4,5,6,7,9\}\) and \(A=\{1,3,5,7,9\}\), what is (A')?
#sets
#universal_set
#odd_even
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A ({2,4,6})
B ({1,3,5,7,9})
C ({2,4,6,8})
D ({9})
Explanation opens after your attempt
Correct Answer
A. ({2,4,6})
Step 1
Concept
After removing the elements of (A) from (U), (2,4,6) remain. This is (A').
Step 2
Why this answer is correct
The correct answer is A. ({2,4,6}). After removing the elements of (A) from (U), (2,4,6) remain. This is (A').
Step 3
Exam Tip
(U) से (A) के तत्व हटाने पर (2,4,6) बचते हैं। यही (A') है।
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यदि \(A=\{w,x,y,z\}\) है तो (\mathcal{P}(A)) में कितने तीन तत्व वाले उपसमुच्चय होंगे?
If \(A=\{w,x,y,z\}\), how many three element subsets are in (\mathcal{P}(A))?
#sets
#power_set
#three_element_subsets
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
There are (4) ways to choose three elements from four. So there are (4) three element subsets.
Step 2
Why this answer is correct
The correct answer is C. (4). There are (4) ways to choose three elements from four. So there are (4) three element subsets.
Step 3
Exam Tip
चार तत्वों में से तीन चुनने के (4) तरीके हैं। इसलिए तीन तत्व वाले उपसमुच्चय (4) हैं।
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यदि \(U=\{1,2,3,4,5,6\}\) और (A'={2,6}) है तो (A) क्या है?
If \(U=\{1,2,3,4,5,6\}\) and (A'={2,6}), what is (A)?
#sets
#universal_set
#find_set
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A ({2,6})
B ({1,3,4,5})
C ({1,2,3})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
B. ({1,3,4,5})
Step 1
Concept
If the complement is (2,6), then (A) contains the remaining elements of (U). So \(A=\{1,3,4,5\}\).
Step 2
Why this answer is correct
The correct answer is B. ({1,3,4,5}). If the complement is (2,6), then (A) contains the remaining elements of (U). So \(A=\{1,3,4,5\}\).
Step 3
Exam Tip
यदि पूरक (2,6) है तो (A) में (U) के बाकी तत्व होंगे। इसलिए \(A=\{1,3,4,5\}\) है।
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यदि \(A=\{100,200,300\}\) है तो (A) स्वयं (\mathcal{P}(A)) में क्यों होता है?
If \(A=\{100,200,300\}\), why is (A) itself in (\mathcal{P}(A))?
#sets
#power_set
#self_subset
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A क्योंकि \(A\subseteq A\) / because \(A\subseteq A\)
B क्योंकि \(A=\emptyset\) / because \(A=\emptyset\)
C क्योंकि (A=U) हमेशा / because (A=U) always
D क्योंकि (A) में एक तत्व है / because (A) has one element
Explanation opens after your attempt
Correct Answer
A. क्योंकि \(A\subseteq A\) / because \(A\subseteq A\)
Step 1
Concept
Every set is a subset of itself. Hence \(A\in\mathcal{P}(A)\) is correct.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि \(A\subseteq A\) / because \(A\subseteq A\). Every set is a subset of itself. Hence \(A\in\mathcal{P}(A)\) is correct.
Step 3
Exam Tip
हर समुच्चय स्वयं का उपसमुच्चय होता है। इसलिए \(A\in\mathcal{P}(A)\) सही है।
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यदि \(A=\{7,14,21\}\) है तो (7) और ({7}) में से (\mathcal{P}(A)) का तत्व कौन है?
If \(A=\{7,14,21\}\), which among (7) and ({7}) is an element of (\mathcal{P}(A))?
#sets
#power_set
#common_mistake
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A केवल (7) / only (7)
B केवल ({7}) / only ({7})
C दोनों / both
D कोई नहीं / none
Explanation opens after your attempt
Correct Answer
B. केवल ({7}) / only ({7})
Step 1
Concept
(\mathcal{P}(A)) contains subsets and ({7}) is a subset. (7) is a direct element of (A).
Step 2
Why this answer is correct
The correct answer is B. केवल ({7}) / only ({7}). (\mathcal{P}(A)) contains subsets and ({7}) is a subset. (7) is a direct element of (A).
Step 3
Exam Tip
(\mathcal{P}(A)) में उपसमुच्चय होते हैं और ({7}) एक उपसमुच्चय है। (7) सीधे (A) का तत्व है।
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यदि \(U=\{सेब,केला,अंगूर,आम\}\) और \(A=\{सेब,आम\}\) है तो (A') क्या है?
If \(U=\{apple,banana,grapes,mango\}\) and \(A=\{apple,mango\}\), what is (A')?
#sets
#universal_set
#real_context
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A ({सेब,आम}) / ({apple,mango})
B ({केला,अंगूर}) / ({banana,grapes})
C ({अंगूर,आम}) / ({grapes,mango})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
B. ({केला,अंगूर}) / ({banana,grapes})
Step 1
Concept
(A') contains the fruits in (U) that are not in (A). So banana and grapes are correct.
Step 2
Why this answer is correct
The correct answer is B. ({केला,अंगूर}) / ({banana,grapes}). (A') contains the fruits in (U) that are not in (A). So banana and grapes are correct.
Step 3
Exam Tip
(A') में (U) के वे फल होंगे जो (A) में नहीं हैं। इसलिए केला और अंगूर सही हैं।
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यदि \(A=\{2,3,4,5,6\}\) है तो (\mathcal{P}(A)) में कितने चार तत्व वाले उपसमुच्चय होंगे?
If \(A=\{2,3,4,5,6\}\), how many four element subsets are in (\mathcal{P}(A))?
#sets
#power_set
#four_element_subsets
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A (4)
B (5)
C (10)
D (16)
Explanation opens after your attempt
Step 1
Concept
There are (5) ways to choose four elements from five. In each subset one different element is left out.
Step 2
Why this answer is correct
The correct answer is B. (5). There are (5) ways to choose four elements from five. In each subset one different element is left out.
Step 3
Exam Tip
पांच तत्वों में से चार चुनने के (5) तरीके हैं। हर उपसमुच्चय में एक अलग तत्व छूटता है।
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यदि \(A=\{d,e,f\}\) है तो \(\emptyset\) (\mathcal{P}(A)) में क्यों होता है?
If \(A=\{d,e,f\}\), why is \(\emptyset\) in (\mathcal{P}(A))?
#sets
#power_set
#empty_subset
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A क्योंकि \(\emptyset\subseteq A\) / because \(\emptyset\subseteq A\)
B क्योंकि \(\emptyset=A\) / because \(\emptyset=A\)
C क्योंकि \(\emptyset=U\) / because \(\emptyset=U\)
D क्योंकि \(\emptyset\) संख्या है / because \(\emptyset\) is a number
Explanation opens after your attempt
Correct Answer
A. क्योंकि \(\emptyset\subseteq A\) / because \(\emptyset\subseteq A\)
Step 1
Concept
\(\emptyset\) is a subset of every set. Therefore it is an element of every power set.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि \(\emptyset\subseteq A\) / because \(\emptyset\subseteq A\). \(\emptyset\) is a subset of every set. Therefore it is an element of every power set.
Step 3
Exam Tip
\(\emptyset\) हर समुच्चय का उपसमुच्चय होता है। इसलिए यह हर घात समुच्चय का तत्व होता है।
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यदि \(U=\{1,2,3,4,5,6,7\}\) और \(A=\{2,4,7\}\) है तो (\mathcal{P}(A')) में कितने तत्व होंगे?
If \(U=\{1,2,3,4,5,6,7\}\) and \(A=\{2,4,7\}\), how many elements will be in (\mathcal{P}(A'))?
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#power_set
#complement_power
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A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
First (A'={1,3,5,6}), which has (4) elements. So (\mathcal{P}(A')) has \(2^4=16\) elements.
Step 2
Why this answer is correct
The correct answer is C. (16). First (A'={1,3,5,6}), which has (4) elements. So (\mathcal{P}(A')) has \(2^4=16\) elements.
Step 3
Exam Tip
पहले (A'={1,3,5,6}) है जिसमें (4) तत्व हैं। इसलिए (\mathcal{P}(A')) में \(2^4=16\) तत्व होंगे।
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यदि \(A=\{{2},4,6\}\) है तो (n(A)) कितना है?
If \(A=\{{2},4,6\}\), what is (n(A))?
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#nested_set
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A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
({2}) is one separate element and (4,6) are two other elements. So (A) has (3) elements.
Step 2
Why this answer is correct
The correct answer is B. (3). ({2}) is one separate element and (4,6) are two other elements. So (A) has (3) elements.
Step 3
Exam Tip
({2}) एक अलग तत्व है और (4,6) दो अन्य तत्व हैं। इसलिए (A) में (3) तत्व हैं।
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यदि \(A=\{{2},4,6\}\) है तो (n(\mathcal{P}(A))) कितना होगा?
If \(A=\{{2},4,6\}\), what is (n(\mathcal{P}(A)))?
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#nested_cardinality
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A (4)
B (6)
C (8)
D (12)
Explanation opens after your attempt
Step 1
Concept
Set (A) has (3) elements so its power set has \(2^3=8\) elements. Count brackets carefully.
Step 2
Why this answer is correct
The correct answer is C. (8). Set (A) has (3) elements so its power set has \(2^3=8\) elements. Count brackets carefully.
Step 3
Exam Tip
(A) में (3) तत्व हैं इसलिए घात समुच्चय में \(2^3=8\) तत्व होंगे। कोष्ठकों को ध्यान से गिनें।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(A=\{3,4\}\) है तो (\mathcal{P}(A')) किस समुच्चय के उपसमुच्चयों से बनेगा?
If \(U=\{1,2,3,4,5,6\}\) and \(A=\{3,4\}\), (\mathcal{P}(A')) will be made from subsets of which set?
#sets
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#complement_basis
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A ({3,4})
B ({1,2,5,6})
C ({1,2,3,4,5,6})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
B. ({1,2,5,6})
Step 1
Concept
First find (A'={1,2,5,6}). Then its power set is formed from subsets of this set.
Step 2
Why this answer is correct
The correct answer is B. ({1,2,5,6}). First find (A'={1,2,5,6}). Then its power set is formed from subsets of this set.
Step 3
Exam Tip
पहले (A'={1,2,5,6}) निकालते हैं। फिर उसका घात समुच्चय इसी के उपसमुच्चयों से बनेगा।
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यदि \(A=\{1,4,7,10\}\) है तो (\mathcal{P}(A)) में शून्य तत्व वाला उपसमुच्चय कितने हैं?
If \(A=\{1,4,7,10\}\), how many zero element subsets are in (\mathcal{P}(A))?
#sets
#power_set
#zero_element_subset
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A (0)
B (1)
C (4)
D (16)
Explanation opens after your attempt
Step 1
Concept
The only zero element subset is \(\emptyset\). Therefore the number of such subsets is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). The only zero element subset is \(\emptyset\). Therefore the number of such subsets is (1).
Step 3
Exam Tip
शून्य तत्व वाला उपसमुच्चय केवल \(\emptyset\) है। इसलिए ऐसे उपसमुच्चय की संख्या (1) होती है।
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यदि \(U=\{2,3,4,5,6,7,8,9\}\) और \(A=\{2,3,4,5\}\) है तो (A') में सबसे बड़ी संख्या कौन सी है?
If \(U=\{2,3,4,5,6,7,8,9\}\) and \(A=\{2,3,4,5\}\), what is the largest number in (A')?
#sets
#universal_set
#largest_element
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A (5)
B (6)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(A') contains (6,7,8,9). The largest among these is (9).
Step 2
Why this answer is correct
The correct answer is D. (9). (A') contains (6,7,8,9). The largest among these is (9).
Step 3
Exam Tip
(A') में (6,7,8,9) होंगे। इनमें सबसे बड़ी संख्या (9) है।
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यदि \(A=\{क,ख,ग,घ\}\) है तो ({क,घ}) (\mathcal{P}(A)) में क्यों होगा?
If \(A=\{a,b,c,d\}\), why will ({a,d}) be in (\mathcal{P}(A))?
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#power_set
#reasoning
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A क्योंकि यह (A) का उपसमुच्चय है / because it is a subset of (A)
B क्योंकि यह (A) का पूरक है / because it is the complement of (A)
C क्योंकि यह सार्वत्रिक समुच्चय है / because it is the universal set
D क्योंकि यह रिक्त समुच्चय है / because it is the empty set
Explanation opens after your attempt
Correct Answer
A. क्योंकि यह (A) का उपसमुच्चय है / because it is a subset of (A)
Step 1
Concept
All elements of ({a,d}) are in (A), so it is a subset. A power set contains all subsets.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि यह (A) का उपसमुच्चय है / because it is a subset of (A). All elements of ({a,d}) are in (A), so it is a subset. A power set contains all subsets.
Step 3
Exam Tip
({क,घ}) के सभी तत्व (A) में हैं इसलिए यह उपसमुच्चय है। घात समुच्चय में सभी उपसमुच्चय आते हैं।
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यदि \(U=\{3,6,9,12\}\) और (A=U) है तो (A') में कितने तत्व हैं?
If \(U=\{3,6,9,12\}\) and (A=U), how many elements are in (A')?
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#universal_set
#empty_complement
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A (0)
B (1)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
When (A=U), no element remains outside (A) in (U). Therefore (A') is empty.
Step 2
Why this answer is correct
The correct answer is A. (0). When (A=U), no element remains outside (A) in (U). Therefore (A') is empty.
Step 3
Exam Tip
जब (A=U) होता है तो (U) में (A) से बाहर कोई तत्व नहीं बचता। इसलिए (A') रिक्त है।
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यदि \(U=\{2,4,6\}\) और \(A=\emptyset\) है तो (\mathcal{P}(A')) में कितने तत्व होंगे?
If \(U=\{2,4,6\}\) and \(A=\emptyset\), how many elements will be in (\mathcal{P}(A'))?
#sets
#power_set
#empty_set_complement
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A (3)
B (6)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
When \(A=\emptyset\), (A'=U). Here (U) has (3) elements so the power set has \(2^3=8\) elements.
Step 2
Why this answer is correct
The correct answer is C. (8). When \(A=\emptyset\), (A'=U). Here (U) has (3) elements so the power set has \(2^3=8\) elements.
Step 3
Exam Tip
जब \(A=\emptyset\) हो तो (A'=U) होता है। यहां (U) में (3) तत्व हैं इसलिए \(2^3=8\) तत्व मिलेंगे।
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यदि \(A=\{2,5,8\}\) है तो (\mathcal{P}(A)) में कुल कितने उपसमुच्चय (5) को रखते हैं?
If \(A=\{2,5,8\}\), how many subsets in (\mathcal{P}(A)) contain (5)?
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#power_set
#contains_element
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
Keep (5) fixed and choose from the remaining (2) elements in \(2^2=4\) ways. So there are (4) such subsets.
Step 2
Why this answer is correct
The correct answer is C. (4). Keep (5) fixed and choose from the remaining (2) elements in \(2^2=4\) ways. So there are (4) such subsets.
Step 3
Exam Tip
(5) को स्थिर रखकर बाकी (2) तत्वों के लिए \(2^2=4\) विकल्प हैं। इसलिए ऐसे (4) उपसमुच्चय होंगे।
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यदि \(U=\{नीला,हरा,पीला,गुलाबी\}\) और \(A=\{हरा,गुलाबी\}\) है तो (A') क्या है?
If \(U=\{blue,green,yellow,pink\}\) and \(A=\{green,pink\}\), what is (A')?
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#universal_set
#color_context
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A ({हरा,गुलाबी}) / ({green,pink})
B ({नीला,पीला}) / ({blue,yellow})
C ({नीला,हरा}) / ({blue,green})
D ({पीला,गुलाबी}) / ({yellow,pink})
Explanation opens after your attempt
Correct Answer
B. ({नीला,पीला}) / ({blue,yellow})
Step 1
Concept
After removing the colors of (A), blue and yellow remain in (U). Hence (A'={blue,yellow}).
Step 2
Why this answer is correct
The correct answer is B. ({नीला,पीला}) / ({blue,yellow}). After removing the colors of (A), blue and yellow remain in (U). Hence (A'={blue,yellow}).
Step 3
Exam Tip
(A) के रंग हटाने पर (U) में नीला और पीला बचते हैं। इसलिए (A'={नीला,पीला}) है।
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यदि \(A=\{12,24,36\}\) है तो (\mathcal{P}(A)) में कितने उपसमुच्चय (36) को नहीं रखते?
If \(A=\{12,24,36\}\), how many subsets in (\mathcal{P}(A)) do not contain (36)?
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#power_set
#without_element
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A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
After excluding (36), the remaining (2) elements form \(2^2=4\) subsets. Count the remaining elements in such questions.
Step 2
Why this answer is correct
The correct answer is C. (4). After excluding (36), the remaining (2) elements form \(2^2=4\) subsets. Count the remaining elements in such questions.
Step 3
Exam Tip
(36) को हटाकर बाकी (2) तत्वों से \(2^2=4\) उपसमुच्चय बनते हैं। ऐसे प्रश्नों में बचे तत्व गिनें।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\) और \(T=\{3,6,9\}\) है तो (T') में कौन सा तत्व नहीं होगा?
If \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(T=\{3,6,9\}\), which element will not be in (T')?
#sets
#universal_set
#element_membership
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A (1)
B (2)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
Elements of the original set (T) do not appear in the complement. So (6) will not be in (T').
Step 2
Why this answer is correct
The correct answer is C. (6). Elements of the original set (T) do not appear in the complement. So (6) will not be in (T').
Step 3
Exam Tip
पूरक में मूल समुच्चय (T) के तत्व नहीं आते। इसलिए (6) (T') में नहीं होगा।
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यदि \(A=\{o,u,i\}\) है तो (\mathcal{P}(A)) में कितने तीन तत्व वाले उपसमुच्चय होंगे?
If \(A=\{o,u,i\}\), how many three element subsets are in (\mathcal{P}(A))?
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#power_set
#whole_subset_count
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A (1)
B (2)
C (3)
D (6)
Explanation opens after your attempt
Step 1
Concept
The only three element subset of a three element set is the whole set. So the number is (1).
Step 2
Why this answer is correct
The correct answer is A. (1). The only three element subset of a three element set is the whole set. So the number is (1).
Step 3
Exam Tip
तीन तत्वों वाले समुच्चय का तीन तत्व वाला उपसमुच्चय केवल पूरा समुच्चय होता है। इसलिए संख्या (1) है।
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यदि \(A=\{5,6\}\) है तो कौन सा कथन सही है?
If \(A=\{5,6\}\), which statement is correct?
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#power_set
#statement
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A \({5}\subseteq A\) और \({5}\in\mathcal{P}(A)\) / \({5}\subseteq A\) and \({5}\in\mathcal{P}(A)\)
B \(5\in\mathcal{P}(A)\) केवल / \(5\in\mathcal{P}(A)\) only
C \({7}\in\mathcal{P}(A)\)
D (\mathcal{P}(A)=A)
Explanation opens after your attempt
Correct Answer
A. \({5}\subseteq A\) और \({5}\in\mathcal{P}(A)\) / \({5}\subseteq A\) and \({5}\in\mathcal{P}(A)\)
Step 1
Concept
({5}) is a subset of (A), so it is an element of the power set. Do not treat direct (5) as an element of the power set.
Step 2
Why this answer is correct
The correct answer is A. \({5}\subseteq A\) और \({5}\in\mathcal{P}(A)\) / \({5}\subseteq A\) and \({5}\in\mathcal{P}(A)\). ({5}) is a subset of (A), so it is an element of the power set. Do not treat direct (5) as an element of the power set.
Step 3
Exam Tip
({5}) (A) का उपसमुच्चय है इसलिए यह घात समुच्चय का तत्व है। सीधे (5) को घात समुच्चय का तत्व न मानें।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\) और \(A=\{1,4,6,8\}\) है तो (A') में कितने तत्व (5) से छोटे हैं?
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{1,4,6,8\}\), how many elements of (A') are less than (5)?
#sets
#universal_set
#comparison
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(A'={2,3,5,7}). Among these, (2) and (3) are less than (5).
Step 2
Why this answer is correct
The correct answer is B. (2). (A'={2,3,5,7}). Among these, (2) and (3) are less than (5).
Step 3
Exam Tip
(A'={2,3,5,7}) है। इनमें (5) से छोटे (2) और (3) हैं।
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यदि \(A=\{4,5\}\) है तो (\mathcal{P}(\mathcal{P}(A))) में कितने तत्व होंगे?
If \(A=\{4,5\}\), how many elements are in (\mathcal{P}(\mathcal{P}(A)))?
#sets
#power_set
#double_power_set
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A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
First (n(\mathcal{P}(A))=22 =4). Then (\mathcal{P}(\mathcal{P}(A))) has \(2^4=16\) elements.
Step 2
Why this answer is correct
The correct answer is C. (16). First (n(\mathcal{P}(A))=22 =4). Then (\mathcal{P}(\mathcal{P}(A))) has \(2^4=16\) elements.
Step 3
Exam Tip
पहले (n(\mathcal{P}(A))=22 =4) है। फिर (\mathcal{P}(\mathcal{P}(A))) में \(2^4=16\) तत्व होंगे।
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यदि \(U=\{2,4,6,8,10\}\) और \(A=\{2,10\}\) है तो ((A')') क्या है?
If \(U=\{2,4,6,8,10\}\) and \(A=\{2,10\}\), what is ((A')')?
#sets
#universal_set
#double_complement
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A ({2,10})
B ({4,6,8})
C ({2,4,6,8,10})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
A. ({2,10})
Step 1
Concept
The complement of a complement is the original set. Hence ((A')'=A={2,10}).
Step 2
Why this answer is correct
The correct answer is A. ({2,10}). The complement of a complement is the original set. Hence ((A')'=A={2,10}).
Step 3
Exam Tip
पूरक का पूरक मूल समुच्चय होता है। इसलिए ((A')'=A={2,10}) है।
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यदि \(A=\{1,3,9\}\) है तो (\mathcal{P}(A)) में कितने उपसमुच्चय ({1,9}) को शामिल करेंगे?
If \(A=\{1,3,9\}\), how many subsets in (\mathcal{P}(A)) will include ({1,9})?
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#include_subset
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Keeping (1) and (9) is fixed and (3) can be taken or not taken in (2) ways. So there are (2) such subsets.
Step 2
Why this answer is correct
The correct answer is B. (2). Keeping (1) and (9) is fixed and (3) can be taken or not taken in (2) ways. So there are (2) such subsets.
Step 3
Exam Tip
(1) और (9) रखना तय है और (3) को लेने या न लेने के (2) तरीके हैं। इसलिए ऐसे (2) उपसमुच्चय हैं।
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यदि \(U=\{सभी एक अंकीय प्राकृतिक संख्याएं\}\) और \(A=\{2,4,6,8\}\) है तो (A') क्या है?
If \(U=\{all one digit natural numbers\}\) and \(A=\{2,4,6,8\}\), what is (A')?
#sets
#universal_set
#natural_numbers
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A ({1,3,5,7,9})
B ({0,1,3,5,7,9})
C ({2,4,6,8})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,7,9})
Step 1
Concept
One digit natural numbers are from (1) to (9). After removing (A), (1,3,5,7,9) remain.
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,7,9}). One digit natural numbers are from (1) to (9). After removing (A), (1,3,5,7,9) remain.
Step 3
Exam Tip
एक अंकीय प्राकृतिक संख्याएं (1) से (9) तक हैं। (A) हटाने पर (1,3,5,7,9) बचते हैं।
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यदि \(A=\{1,2,3,4\}\) है तो (\mathcal{P}(A)) में कितने उपसमुच्चय (2) को रखते और (3) को नहीं रखते?
If \(A=\{1,2,3,4\}\), how many subsets in (\mathcal{P}(A)) contain (2) and do not contain (3)?
#sets
#power_set
#condition_count
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
Taking (2) and not taking (3) are fixed. For remaining (1,4), there are \(2^2=4\) choices.
Step 2
Why this answer is correct
The correct answer is B. (4). Taking (2) and not taking (3) are fixed. For remaining (1,4), there are \(2^2=4\) choices.
Step 3
Exam Tip
(2) लेना और (3) न लेना तय है। बाकी (1,4) के लिए \(2^2=4\) विकल्प हैं।
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यदि \(U=\{1,2,3,4,5,6,7\}\), \(A=\{2,5,7\}\) और (B=A') है तो (B') क्या है?
If \(U=\{1,2,3,4,5,6,7\}\), \(A=\{2,5,7\}\) and (B=A'), what is (B')?
#sets
#universal_set
#double_complement
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A ({2,5,7})
B ({1,3,4,6})
C ({1,2,3,4,5,6,7})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
A. ({2,5,7})
Step 1
Concept
If (B=A'), then (B'=(A')'=A). Therefore (B'={2,5,7}).
Step 2
Why this answer is correct
The correct answer is A. ({2,5,7}). If (B=A'), then (B'=(A')'=A). Therefore (B'={2,5,7}).
Step 3
Exam Tip
यदि (B=A') है तो (B'=(A')'=A) होगा। इसलिए (B'={2,5,7}) है।
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यदि \(A={\emptyset,{\emptyset},0}\) है तो (n(\mathcal{P}(A))) कितना होगा?
If \(A={\emptyset,{\emptyset},0}\), what is (n(\mathcal{P}(A)))?
#sets
#power_set
#nested_empty
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A (4)
B (6)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
(A) has three distinct elements \(\emptyset,{\emptyset},0\). Therefore (n(\mathcal{P}(A))=23 =8).
Step 2
Why this answer is correct
The correct answer is C. (8). (A) has three distinct elements \(\emptyset,{\emptyset},0\). Therefore (n(\mathcal{P}(A))=23 =8).
Step 3
Exam Tip
(A) में तीन अलग तत्व \(\emptyset,{\emptyset},0\) हैं। इसलिए (n(\mathcal{P}(A))=23 =8) है।
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यदि \(U=\{5,10,15,20,25,30\}\) और \(A=\{10,20,30\}\) है तो (A') क्या है?
If \(U=\{5,10,15,20,25,30\}\) and \(A=\{10,20,30\}\), what is (A')?
#sets
#universal_set
#complement
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A ({5,15,25})
B ({10,20,30})
C ({5,10,15})
D ({25,30})
Explanation opens after your attempt
Correct Answer
A. ({5,15,25})
Step 1
Concept
After removing (10,20,30) from (U), (5,15,25) remain. This is the complement.
Step 2
Why this answer is correct
The correct answer is A. ({5,15,25}). After removing (10,20,30) from (U), (5,15,25) remain. This is the complement.
Step 3
Exam Tip
(U) से (10,20,30) हटाने पर (5,15,25) बचते हैं। यही पूरक है।
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यदि \(A=\{2,4,6,8\}\) है तो कुल उपसमुच्चयों की संख्या और दो तत्व वाले उपसमुच्चयों की संख्या क्रमशः क्या है?
If \(A=\{2,4,6,8\}\), what are the total number of subsets and the number of two element subsets respectively?
#sets
#power_set
#mixed_count
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A (8) और (4) / (8) and (4)
B (16) और (6) / (16) and (6)
C (16) और (8) / (16) and (8)
D (4) और (16) / (4) and (16)
Explanation opens after your attempt
Correct Answer
B. (16) और (6) / (16) and (6)
Step 1
Concept
A set with four elements has \(2^4=16\) total subsets. The number of two element subsets is (6).
Step 2
Why this answer is correct
The correct answer is B. (16) और (6) / (16) and (6). A set with four elements has \(2^4=16\) total subsets. The number of two element subsets is (6).
Step 3
Exam Tip
चार तत्वों वाले समुच्चय के कुल \(2^4=16\) उपसमुच्चय होते हैं। दो तत्व वाले उपसमुच्चय (6) होते हैं।
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यदि \(A=\{a,b,c\}\) है तो (\mathcal{P}(A)) में कितने उपसमुच्चय (a) या (b) में से कम से कम एक को रखते हैं?
If \(A=\{a,b,c\}\), how many subsets in (\mathcal{P}(A)) contain at least one of (a) or (b)?
#sets
#power_set
#at_least_one
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
There are (8) total subsets and (2) subsets contain neither (a) nor (b). So (8-2=6) subsets are correct.
Step 2
Why this answer is correct
The correct answer is C. (6). There are (8) total subsets and (2) subsets contain neither (a) nor (b). So (8-2=6) subsets are correct.
Step 3
Exam Tip
कुल (8) उपसमुच्चय हैं और (a,b) दोनों को न रखने वाले (2) हैं। इसलिए (8-2=6) उपसमुच्चय सही हैं।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(A=\{1,6\}\) है तो \(A'\cap A\) क्या होगा?
If \(U=\{1,2,3,4,5,6\}\) and \(A=\{1,6\}\), what is \(A'\cap A\)?
#sets
#universal_set
#intersection
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A ({1,6})
B ({2,3,4,5})
C \(\emptyset\)
D (U)
Explanation opens after your attempt
Correct Answer
C. \(\emptyset\)
Step 1
Concept
No element can be in both (A) and its complement (A'). Therefore \(A'\cap A=\emptyset\).
Step 2
Why this answer is correct
The correct answer is C. \(\emptyset\). No element can be in both (A) and its complement (A'). Therefore \(A'\cap A=\emptyset\).
Step 3
Exam Tip
कोई तत्व (A) और उसके पूरक (A') दोनों में नहीं हो सकता। इसलिए \(A'\cap A=\emptyset\) है।
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