यदि सार्वत्रिक समुच्चय \(U=\{1,2,3,4,5\}\) और \(A=\{1,3,5\}\) है, तो (A') क्या होगा?
If the universal set is \(U=\{1,2,3,4,5\}\) and \(A=\{1,3,5\}\), what is (A')?
#sets
#complement
#basic
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A (A'={2,4})
B (A'={1,3,5})
C (A'={1,2,3,4,5})
D \(A'=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. (A'={2,4})
Step 1
Concept
(A') contains elements of (U) that are not in (A). In exams, always check (U) first.
Step 2
Why this answer is correct
The correct answer is A. (A'={2,4}). (A') contains elements of (U) that are not in (A). In exams, always check (U) first.
Step 3
Exam Tip
(A') में (U) के वे अवयव आते हैं जो (A) में नहीं हैं। परीक्षा में हमेशा पहले (U) देखें।
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\(यदि (U={1,2,3,4,5,6,7,8,9,10,11,12}) और (A={x:x\in U,x\) divides 12}) है, तो (A') क्या है?
\(If (U={1,2,3,4,5,6,7,8,9,10,11,12}) and (A={x:x\in U,x\) divides 12}), what is (A')?
#sets
#complement
#divisors
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A (A'={5,7,8,9,10,11})
B (A'={1,2,3,4,6,12})
C (A'={2,4,6,8,10,12})
D (A'=U)
Explanation opens after your attempt
Correct Answer
A. (A'={5,7,8,9,10,11})
Step 1
Concept
(A) contains the divisors (1,2,3,4,6,12) of (12), so the remaining elements are in (A'). First form (A) from the condition.
Step 2
Why this answer is correct
The correct answer is A. (A'={5,7,8,9,10,11}). (A) contains the divisors (1,2,3,4,6,12) of (12), so the remaining elements are in (A'). First form (A) from the condition.
Step 3
Exam Tip
(A) में (12) के भाजक (1,2,3,4,6,12) हैं, इसलिए बाकी अवयव (A') में आते हैं। पहले शर्त से (A) बनाएं।
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यदि \(U=\{a,b,c,d\}\) और \(B=\{b,d\}\) है, तो (B') ज्ञात कीजिए।
If \(U=\{a,b,c,d\}\) and \(B=\{b,d\}\), find (B').
#sets
#complement
#letters
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A (B'={a,c})
B (B'={b,d})
C (B'={a,b,c,d})
D \(B'=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. (B'={a,c})
Step 1
Concept
(B') is found by removing elements of (B) from (U). While finding complement, treat (U) as the outer set.
Step 2
Why this answer is correct
The correct answer is A. (B'={a,c}). (B') is found by removing elements of (B) from (U). While finding complement, treat (U) as the outer set.
Step 3
Exam Tip
(B') में (U) से (B) के अवयव हटाए जाते हैं। पूरक निकालते समय बाहरी समुच्चय को (U) मानें।
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\(यदि (U={\)सोमवार,मंगलवार,बुधवार,गुरुवार,शुक्रवार,शनिवार,रविवार\(}) और (W={\)शनिवार,रविवार}) है, तो (W') क्या होगा?
\(If (U={\)Monday,Tuesday,Wednesday,Thursday,Friday,Saturday,Sunday\(}) and (W={\)Saturday,Sunday}), what will (W') be?
#sets
#complement
#word_set
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A \((W'={\)सोमवार,मंगलवार,बुधवार,गुरुवार,शुक्रवार}) / \((W'={\)Monday,Tuesday,Wednesday,Thursday,Friday})
B \((W'={\)शनिवार,रविवार}) / \((W'={\)Saturday,Sunday})
C (W'=U)
D \(W'=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \((W'={\)सोमवार,मंगलवार,बुधवार,गुरुवार,शुक्रवार}) / \((W'={\)Monday,Tuesday,Wednesday,Thursday,Friday})
Step 1
Concept
(W) is the set of weekend days, so (W') contains the other five days. Always find complement with respect to (U).
Step 2
Why this answer is correct
\(The correct answer is A. (W'={\)सोमवार,मंगलवार,बुधवार,गुरुवार,शुक्रवार\(}) / (W'={\)Monday,Tuesday,Wednesday,Thursday,Friday}). (W) is the set of weekend days, so (W') contains the other five days. Always find complement with respect to (U).
Step 3
Exam Tip
(W) सप्ताहांत के दिनों का समुच्चय है, इसलिए (W') में बाकी पांच दिन आएंगे। पूरक हमेशा (U) के संदर्भ में निकालें।
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यदि \(U=\{2,4,6,8,10\}\) और \(A=\{4,8\}\) है, तो (A') कौन सा है?
If \(U=\{2,4,6,8,10\}\) and \(A=\{4,8\}\), which one is (A')?
#sets
#complement
#numerical
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A (A'={2,6,10})
B (A'={4,8})
C (A'={2,4,6,8,10})
D (A'={6,10})
Explanation opens after your attempt
Correct Answer
A. (A'={2,6,10})
Step 1
Concept
Since (A) has (4) and (8), the remaining (2,6,10) are in the complement. Do not mistakenly choose (A) itself.
Step 2
Why this answer is correct
The correct answer is A. (A'={2,6,10}). Since (A) has (4) and (8), the remaining (2,6,10) are in the complement. Do not mistakenly choose (A) itself.
Step 3
Exam Tip
(A) में (4) और (8) हैं, इसलिए शेष (2,6,10) पूरक में होंगे। गलती से (A) को ही उत्तर न मानें।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,3,4\}\) और \(B=\{6,7\}\) है, तो (\(A\cup B\)') क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,3,4\}\), and \(B=\{6,7\}\), what is (\(A\cup B\)')?
#sets
#union_complement
#application
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A ({5,8,9})
B ({1,2,3,4,6,7})
C ({5,6,7,8,9})
D ({1,2,3,4})
Explanation opens after your attempt
Correct Answer
A. ({5,8,9})
Step 1
Concept
\(A\cup B={1,2,3,4,6,7}\), so the remaining (5,8,9) in (U) are the complement. Finding the union first is necessary.
Step 2
Why this answer is correct
The correct answer is A. ({5,8,9}). \(A\cup B={1,2,3,4,6,7}\), so the remaining (5,8,9) in (U) are the complement. Finding the union first is necessary.
Step 3
Exam Tip
\(A\cup B={1,2,3,4,6,7}\), इसलिए (U) में बचे (5,8,9) पूरक हैं। पहले संघ निकालना जरूरी है।
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यदि \(U={x:x\in \mathbb{N},x\le 6}\) और \(A=\{1,2,3\}\) है, तो (A') क्या है?
If \(U={x:x\in \mathbb{N},x\le 6}\) and \(A=\{1,2,3\}\), what is (A')?
#sets
#set_builder
#complement
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A (A'={4,5,6})
B (A'={1,2,3})
C (A'={0,4,5,6})
D (A'={1,2,3,4,5,6})
Explanation opens after your attempt
Correct Answer
A. (A'={4,5,6})
Step 1
Concept
Here \(U=\{1,2,3,4,5,6\}\), and after removing (A), (4,5,6) remain. Read the limit of \(\mathbb{N}\) carefully.
Step 2
Why this answer is correct
The correct answer is A. (A'={4,5,6}). Here \(U=\{1,2,3,4,5,6\}\), and after removing (A), (4,5,6) remain. Read the limit of \(\mathbb{N}\) carefully.
Step 3
Exam Tip
यहाँ \(U=\{1,2,3,4,5,6\}\) है और (A) हटाने पर (4,5,6) बचते हैं। \(\mathbb{N}\) की सीमा ध्यान से पढ़ें।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{2,4,6,8\}\) और \(B=\{1,2,3,4\}\) है, तो (\(A\cap B\)') क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{2,4,6,8\}\), and \(B=\{1,2,3,4\}\), what will (\(A\cap B\)') be?
#sets
#intersection_complement
#application
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A ({1,3,5,6,7,8,9,10})
B ({2,4})
C ({5,6,7,8,9,10})
D ({1,2,3,4,6,8})
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,6,7,8,9,10})
Step 1
Concept
\(A\cap B={2,4}\), so its complement is (U-{2,4}). Take complement only after finding the intersection.
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,6,7,8,9,10}). \(A\cap B={2,4}\), so its complement is (U-{2,4}). Take complement only after finding the intersection.
Step 3
Exam Tip
\(A\cap B={2,4}\), इसलिए इसका पूरक (U-{2,4}) है। प्रतिच्छेद के बाद ही पूरक लें।
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यदि \(U={x:x\in \mathbb{Z},-2\le x\le 2}\) और \(A=\{-1,0,1\}\) है, तो (A') ज्ञात करें।
If \(U={x:x\in \mathbb{Z},-2\le x\le 2}\) and \(A=\{-1,0,1\}\), find (A').
#sets
#integers
#complement
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A (A'={-2,2})
B (A'={-1,0,1})
C (A'={-2,-1,0,1,2})
D (A'={2})
Explanation opens after your attempt
Correct Answer
A. (A'={-2,2})
Step 1
Concept
(U) contains (-2,-1,0,1,2), and removing (A) leaves (-2,2). Both endpoints of the interval are included.
Step 2
Why this answer is correct
The correct answer is A. (A'={-2,2}). (U) contains (-2,-1,0,1,2), and removing (A) leaves (-2,2). Both endpoints of the interval are included.
Step 3
Exam Tip
(U) में (-2,-1,0,1,2) हैं और (A) हटाने पर (-2,2) बचते हैं। अंतराल की दोनों सीमाएं शामिल हैं।
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यदि (n(U)=64) और (n(A')=19) है, तो (n(A)) क्या होगा?
If (n(U)=64) and (n(A')=19), what will (n(A)) be?
#sets
#cardinality
#reverse_complement
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A (45)
B (83)
C (19)
D (64)
Explanation opens after your attempt
Step 1
Concept
(n(A)=n(U)-n(A')=64-19=45). If the complement count is given, subtract it from the total.
Step 2
Why this answer is correct
The correct answer is A. (45). (n(A)=n(U)-n(A')=64-19=45). If the complement count is given, subtract it from the total.
Step 3
Exam Tip
(n(A)=n(U)-n(A')=64-19=45)। पूरक की संख्या दी हो तो कुल में से घटाएं।
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यदि \(A\subseteq U\) और (A'=U) है, तो (A) क्या होना चाहिए?
If \(A\subseteq U\) and (A'=U), what must (A) be?
#sets
#empty_set
#property
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A \(A=\varnothing\)
B (A=U)
C (A=A')
D \(A\ne \varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(A=\varnothing\)
Step 1
Concept
If (A') is the whole (U), then (A) cannot have any element. Hence \(A=\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(A=\varnothing\). If (A') is the whole (U), then (A) cannot have any element. Hence \(A=\varnothing\).
Step 3
Exam Tip
यदि (A') पूरा (U) है, तो (A) में कोई अवयव नहीं हो सकता। इसलिए \(A=\varnothing\) है।
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यदि \(U=\{p,q,r\}\) और \(A=\varnothing\) है, तो (A') क्या है?
If \(U=\{p,q,r\}\) and \(A=\varnothing\), what is (A')?
#sets
#empty_set
#complement
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A (A'=U)
B \(A'=\varnothing\)
C (A'={p})
D (A'={q,r})
Explanation opens after your attempt
Step 1
Concept
The empty set has no elements, so its complement is the whole (U). Remember \(\varnothing'=U\).
Step 2
Why this answer is correct
The correct answer is A. (A'=U). The empty set has no elements, so its complement is the whole (U). Remember \(\varnothing'=U\).
Step 3
Exam Tip
खाली समुच्चय में कोई अवयव नहीं होता, इसलिए उसका पूरक पूरा (U) होता है। याद रखें \(\varnothing'=U\)।
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\(यदि (U={x:x\in \mathbb{N},1\le x\le 14}) और (A={x:x\in U,x\) is odd}) है, तो (n(A')) कितना है?
\(If (U={x:x\in \mathbb{N},1\le x\le 14}) and (A={x:x\in U,x\) is odd}), what is (n(A'))?
#sets
#cardinality
#even_odd
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A (7)
B (14)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(A') contains the even numbers from (1) to (14), and their count is (7). Here the complement of odd is even.
Step 2
Why this answer is correct
The correct answer is A. (7). (A') contains the even numbers from (1) to (14), and their count is (7). Here the complement of odd is even.
Step 3
Exam Tip
(A') में (1) से (14) तक की सम संख्याएं आएंगी, जिनकी संख्या (7) है। विषम का पूरक यहां सम है।
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किसी समुच्चय (A) के लिए ((A')') किसके बराबर होता है?
For any set (A), what is ((A')') equal to?
#sets
#double_complement
#property
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A (A)
B (A')
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The complement of the complement is the original set (A). This is the important double complement law.
Step 2
Why this answer is correct
The correct answer is A. (A). The complement of the complement is the original set (A). This is the important double complement law.
Step 3
Exam Tip
पूरक का पूरक मूल समुच्चय (A) होता है। यह दोहरे पूरक का महत्वपूर्ण नियम है।
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यदि \(U=\{1,2,3,4,5,6,7\}\) और (A'={2,4,6}) है, तो (A) क्या होगा?
If \(U=\{1,2,3,4,5,6,7\}\) and (A'={2,4,6}), what is (A)?
#sets
#reverse_complement
#numerical
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A \(A=\{1,3,5,7\}\)
B \(A=\{2,4,6\}\)
C (A=U)
D \(A=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(A=\{1,3,5,7\}\)
Step 1
Concept
If (A') is given, removing (A') from (U) gives (A). Even in reverse complement questions, (U) is necessary.
Step 2
Why this answer is correct
The correct answer is A. \(A=\{1,3,5,7\}\). If (A') is given, removing (A') from (U) gives (A). Even in reverse complement questions, (U) is necessary.
Step 3
Exam Tip
यदि (A') दिया हो, तो (U) से (A') हटाकर (A) मिलता है। पूरक उल्टा पढ़ने पर भी (U) जरूरी है।
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यदि \(U=\{a,e,i,o,u\}\) और (V'={e,o}) है, तो (V) क्या है?
If \(U=\{a,e,i,o,u\}\) and (V'={e,o}), what is (V)?
#sets
#reverse_complement
#letters
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A \(V=\{a,i,u\}\)
B \(V=\{e,o\}\)
C (V=U)
D \(V=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(V=\{a,i,u\}\)
Step 1
Concept
(V') contains (e,o), so the remaining (a,i,u) in (U) form (V). In such questions, first remove the given complement.
Step 2
Why this answer is correct
The correct answer is A. \(V=\{a,i,u\}\). (V') contains (e,o), so the remaining (a,i,u) in (U) form (V). In such questions, first remove the given complement.
Step 3
Exam Tip
(V') में (e,o) हैं, इसलिए (U) में बचे (a,i,u) ही (V) हैं। ऐसे प्रश्नों में दिए गए पूरक को पहले हटाएं।
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\(यदि (U={1,2,3,4,5,6,7,8}) और (A={x:x\in U,x\) is even}) है, तो (A') कौन सा है?
\(If (U={1,2,3,4,5,6,7,8}) and (A={x:x\in U,x\) is even}), which is (A')?
#sets
#set_builder
#even_odd
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A ({1,3,5,7})
B ({2,4,6,8})
C ({1,2,3,4})
D (U)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,7})
Step 1
Concept
(A) is the set of even numbers, so the complement contains odd numbers. Read the condition in set-builder form carefully.
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,7}). (A) is the set of even numbers, so the complement contains odd numbers. Read the condition in set-builder form carefully.
Step 3
Exam Tip
(A) सम संख्याओं का समुच्चय है, इसलिए पूरक विषम संख्याएं होंगी। सेट-बिल्डर में शर्त को ध्यान से पढ़ें।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\) और \(A={x:x\in U,x<5}\) है, तो (A') क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(A={x:x\in U,x<5}\), what is (A')?
#sets
#inequality
#complement
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A ({5,6,7,8,9})
B ({1,2,3,4})
C ({4,5,6,7,8,9})
D ({1,2,3,4,5})
Explanation opens after your attempt
Correct Answer
A. ({5,6,7,8,9})
Step 1
Concept
(A) contains numbers less than (5), namely (1,2,3,4), so the complement starts from (5). The inequality (x<5) does not include (5).
Step 2
Why this answer is correct
The correct answer is A. ({5,6,7,8,9}). (A) contains numbers less than (5), namely (1,2,3,4), so the complement starts from (5). The inequality (x<5) does not include (5).
Step 3
Exam Tip
(A) में (5) से छोटी संख्याएं (1,2,3,4) हैं, इसलिए पूरक (5) से शुरू होगा। असमानता (x<5) में (5) शामिल नहीं होता।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\) और \(A={x:x\in U,x\ge 7}\) है, तो (A') क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A={x:x\in U,x\ge 7}\), what will (A') be?
#sets
#inequality
#greater_equal
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A ({1,2,3,4,5,6})
B ({7,8,9,10})
C ({1,2,3,4,5,6,7})
D ({8,9,10})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4,5,6})
Step 1
Concept
(A) contains (7,8,9,10), so the complement is from (1) to (6). In \(x\ge 7\), (7) is also in (A).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4,5,6}). (A) contains (7,8,9,10), so the complement is from (1) to (6). In \(x\ge 7\), (7) is also in (A).
Step 3
Exam Tip
(A) में (7,8,9,10) हैं, इसलिए पूरक (1) से (6) तक है। \(x\ge 7\) में (7) भी (A) में आएगा।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10,11,12\}\) और \(A=\{3,6,9,12\}\) है, तो (A') में कितने अवयव हैं?
If \(U=\{1,2,3,4,5,6,7,8,9,10,11,12\}\) and \(A=\{3,6,9,12\}\), how many elements are in (A')?
#sets
#cardinality
#complement
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A (8)
B (4)
C (12)
D (6)
Explanation opens after your attempt
Step 1
Concept
(n(U)=12) and (n(A)=4), so (n(A')=12-4=8). Subtract from the total number in (U).
Step 2
Why this answer is correct
The correct answer is A. (8). (n(U)=12) and (n(A)=4), so (n(A')=12-4=8). Subtract from the total number in (U).
Step 3
Exam Tip
(n(U)=12) और (n(A)=4), इसलिए (n(A')=12-4=8)। गणना में (U) की कुल संख्या से घटाएं।
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यदि (n(U)=30) और (n(A)=18) है, तो (n(A')) कितना होगा?
If (n(U)=30) and (n(A)=18), what is (n(A'))?
#sets
#cardinality
#formula
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A (12)
B (18)
C (30)
D (48)
Explanation opens after your attempt
Step 1
Concept
(n(A')=n(U)-n(A)=30-18=12). For complement, subtract rather than add.
Step 2
Why this answer is correct
The correct answer is A. (12). (n(A')=n(U)-n(A)=30-18=12). For complement, subtract rather than add.
Step 3
Exam Tip
(n(A')=n(U)-n(A)=30-18=12)। पूरक में जोड़ नहीं, घटाना होता है।
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यदि (n(U)=50) और (n(A')=22) है, तो (n(A)) ज्ञात कीजिए।
If (n(U)=50) and (n(A')=22), find (n(A)).
#sets
#cardinality
#reverse
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A (28)
B (22)
C (72)
D (50)
Explanation opens after your attempt
Step 1
Concept
(n(A)=n(U)-n(A')=50-22=28). Even when complement is given, subtract from the total.
Step 2
Why this answer is correct
The correct answer is A. (28). (n(A)=n(U)-n(A')=50-22=28). Even when complement is given, subtract from the total.
Step 3
Exam Tip
(n(A)=n(U)-n(A')=50-22=28)। पूरक दिया हो तो भी कुल में से घटाएं।
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यदि (n(A)=15) और (n(A')=35) है, तो (n(U)) क्या होगा?
If (n(A)=15) and (n(A')=35), what is (n(U))?
#sets
#cardinality
#union_property
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A (50)
B (35)
C (20)
D (15)
Explanation opens after your attempt
Step 1
Concept
(A) and (A') together form (U), so (n(U)=15+35=50). This comes from \(A\cup A'=U\).
Step 2
Why this answer is correct
The correct answer is A. (50). (A) and (A') together form (U), so (n(U)=15+35=50). This comes from \(A\cup A'=U\).
Step 3
Exam Tip
(A) और (A') मिलकर (U) बनाते हैं, इसलिए (n(U)=15+35=50)। यह \(A\cup A'=U\) से आता है।
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यदि \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\) और \(B=\{3,4,5\}\) है, तो (\(A\cup B\)') क्या है?
If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), and \(B=\{3,4,5\}\), what is (\(A\cup B\)')?
#sets
#union_complement
#demorgan_intro
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A ({6})
B ({1,2,3,4,5})
C ({1,2})
D ({4,5,6})
Explanation opens after your attempt
Step 1
Concept
\(A\cup B={1,2,3,4,5}\), so its complement is ({6}). First find the union, then take complement.
Step 2
Why this answer is correct
The correct answer is A. ({6}). \(A\cup B={1,2,3,4,5}\), so its complement is ({6}). First find the union, then take complement.
Step 3
Exam Tip
\(A\cup B={1,2,3,4,5}\), इसलिए उसका पूरक ({6}) है। पहले संघ निकालें फिर पूरक लें।
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यदि \(U=\{a,b,c,d,e\}\), \(A=\{a,b,d\}\) और \(B=\{b,c,d\}\) है, तो (\(A\cap B\)') क्या होगा?
If \(U=\{a,b,c,d,e\}\), \(A=\{a,b,d\}\), and \(B=\{b,c,d\}\), what will (\(A\cap B\)') be?
#sets
#intersection_complement
#basic
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A ({a,c,e})
B ({b,d})
C ({a,b,c,d})
D ({e})
Explanation opens after your attempt
Correct Answer
A. ({a,c,e})
Step 1
Concept
\(A\cap B={b,d}\), so the complement is ({a,c,e}). First identify common elements.
Step 2
Why this answer is correct
The correct answer is A. ({a,c,e}). \(A\cap B={b,d}\), so the complement is ({a,c,e}). First identify common elements.
Step 3
Exam Tip
\(A\cap B={b,d}\), इसलिए पूरक ({a,c,e}) है। पहले सामान्य अवयव पहचानें।
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यदि \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3,4\}\) और \(B=\{3,4,5\}\) है, तो \(A'\cap B'\) क्या है?
If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3,4\}\), and \(B=\{3,4,5\}\), what is \(A'\cap B'\)?
#sets
#complement
#intersection
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A ({6})
B ({1,2})
C ({5,6})
D ({3,4})
Explanation opens after your attempt
Step 1
Concept
(A'={5,6}) and (B'={1,2,6}), so the intersection is ({6}). Find complements separately and then combine.
Step 2
Why this answer is correct
The correct answer is A. ({6}). (A'={5,6}) and (B'={1,2,6}), so the intersection is ({6}). Find complements separately and then combine.
Step 3
Exam Tip
(A'={5,6}) और (B'={1,2,6}), इसलिए प्रतिच्छेद ({6}) है। पूरक अलग-अलग निकालकर मिलाएं।
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यदि \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,3,5\}\) और \(B=\{2,3,6\}\) है, तो \(A'\cup B'\) क्या है?
If \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,3,5\}\), and \(B=\{2,3,6\}\), what is \(A'\cup B'\)?
#sets
#complement
#union
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A ({1,2,4,5,6,7})
B ({3})
C ({4,7})
D (U)
Explanation opens after your attempt
Correct Answer
A. ({1,2,4,5,6,7})
Step 1
Concept
(A'={2,4,6,7}) and (B'={1,4,5,7}), so the union is ({1,2,4,5,6,7}). It is also equal to (\(A\cap B\)').
Step 2
Why this answer is correct
The correct answer is A. ({1,2,4,5,6,7}). (A'={2,4,6,7}) and (B'={1,4,5,7}), so the union is ({1,2,4,5,6,7}). It is also equal to (\(A\cap B\)').
Step 3
Exam Tip
(A'={2,4,6,7}) और (B'={1,4,5,7}), इसलिए संघ ({1,2,4,5,6,7}) है। यह (\(A\cap B\)') के बराबर भी है।
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यदि \(A\subseteq U\) है, तो (A') की सबसे सही परिभाषा कौन सी है?
If \(A\subseteq U\), which is the most correct definition of (A')?
#sets
#definition
#set_builder
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A \((A'={x:x\in U\) and \(x\notin A})\)
B \(A'={x:x\in A}\)
C \(A'={x:x\notin U}\)
D \(A'=A\cup U\)
Explanation opens after your attempt
Correct Answer
A. \((A'={x:x\in U\) and \(x\notin A})\)
Step 1
Concept
Complement contains elements that are in (U) but not in (A). Mentioning (U) is necessary in the definition.
Step 2
Why this answer is correct
\(The correct answer is A. (A'={x:x\in U\) and \(x\notin A}). Complement contains elements that are in (U) but not in (A). Mentioning (U) is necessary in the definition.\)
Step 3
Exam Tip
पूरक में वही अवयव होते हैं जो (U) में हैं पर (A) में नहीं हैं। परिभाषा में (U) का उल्लेख जरूरी है।
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यदि \(U=\{1,2,3,4,5\}\) और \(A=\{1,2\}\) है, तो (U-A) किसके बराबर है?
If \(U=\{1,2,3,4,5\}\) and \(A=\{1,2\}\), what is (U-A) equal to?
#sets
#difference
#complement
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A (A')
B (A)
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
(U-A) means removing (A) from (U), which is (A'). Complement can also be written as (U-A).
Step 2
Why this answer is correct
The correct answer is A. (A'). (U-A) means removing (A) from (U), which is (A'). Complement can also be written as (U-A).
Step 3
Exam Tip
(U-A) का अर्थ (U) से (A) हटाना है, यही (A') है। पूरक को (U-A) भी लिख सकते हैं।
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यदि \(A\subseteq B\subseteq U\) है, तो \(B'\subseteq A'\) के बारे में क्या कहा जा सकता है?
If \(A\subseteq B\subseteq U\), what can be said about \(B'\subseteq A'\)?
#sets
#subset
#complement_property
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A यह हमेशा सत्य है / It is always true
B यह हमेशा असत्य है / It is always false
C यह तभी सत्य है जब (A=U) / It is true only when (A=U)
D यह तभी सत्य है जब \(B=\varnothing\) / It is true only when \(B=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. यह हमेशा सत्य है / It is always true
Step 1
Concept
The complement of the larger set is contained in the complement of the smaller set. Inclusion reverses after taking complement.
Step 2
Why this answer is correct
The correct answer is A. यह हमेशा सत्य है / It is always true. The complement of the larger set is contained in the complement of the smaller set. Inclusion reverses after taking complement.
Step 3
Exam Tip
बड़े समुच्चय का पूरक छोटे समुच्चय के पूरक में समाहित होता है। समावेशन पूरक लेने पर उलट जाता है।
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यदि \(A\subseteq U\) है, तो \(A'\subseteq U\) के बारे में कौन सा कथन सही है?
If \(A\subseteq U\), which statement about \(A'\subseteq U\) is correct?
#sets
#subset
#universal
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A \(A'\subseteq U\) हमेशा सत्य है / \(A'\subseteq U\) is always true
B \(A'\subseteq A\) हमेशा सत्य है / \(A'\subseteq A\) is always true
C \(U\subseteq A'\) हमेशा सत्य है / \(U\subseteq A'\) is always true
D (A'=A) हमेशा सत्य है / (A'=A) is always true
Explanation opens after your attempt
Correct Answer
A. \(A'\subseteq U\) हमेशा सत्य है / \(A'\subseteq U\) is always true
Step 1
Concept
All elements of (A') are taken from (U), so \(A'\subseteq U\). Complement never goes outside (U).
Step 2
Why this answer is correct
The correct answer is A. \(A'\subseteq U\) हमेशा सत्य है / \(A'\subseteq U\) is always true. All elements of (A') are taken from (U), so \(A'\subseteq U\). Complement never goes outside (U).
Step 3
Exam Tip
(A') के सभी अवयव (U) से ही लिए जाते हैं, इसलिए \(A'\subseteq U\)। पूरक कभी (U) के बाहर नहीं जाता।
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यदि \(U=\{1,2,3,4,5,6\}\) और (A'={1,6}) है, तो \(A\cup A'\) क्या होगा?
If \(U=\{1,2,3,4,5,6\}\) and (A'={1,6}), what will \(A\cup A'\) be?
#sets
#union_property
#reasoning
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A (U)
B (A)
C (A')
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Every set and its complement together form the whole (U). There is no need to find (A) separately.
Step 2
Why this answer is correct
The correct answer is A. (U). Every set and its complement together form the whole (U). There is no need to find (A) separately.
Step 3
Exam Tip
हर समुच्चय और उसका पूरक मिलकर पूरा (U) बनाते हैं। (A) अलग से निकालने की जरूरत नहीं है।
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यदि \(U=\{1,2,3,4,5\}\) और (A'={2,5}) है, तो \(A\cap A'\) क्या होगा?
If \(U=\{1,2,3,4,5\}\) and (A'={2,5}), what will \(A\cap A'\) be?
#sets
#intersection_property
#reasoning
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A \(\varnothing\)
B (A)
C (A')
D (U)
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\)
Step 1
Concept
No element belongs to both (A) and (A'), so the intersection is empty. This rule applies to every set.
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). No element belongs to both (A) and (A'), so the intersection is empty. This rule applies to every set.
Step 3
Exam Tip
कोई अवयव (A) और (A') दोनों में नहीं होता, इसलिए प्रतिच्छेद खाली है। यह नियम हर समुच्चय पर लागू होता है।
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यदि \(U={x:x\in \mathbb{N},1\le x\le 10}\) और \(P=\{2,3,5,7\}\) है, तो (P') क्या है?
If \(U={x:x\in \mathbb{N},1\le x\le 10}\) and \(P=\{2,3,5,7\}\), what is (P')?
#sets
#prime_numbers
#complement
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A ({1,4,6,8,9,10})
B ({2,3,5,7})
C ({4,6,8,9,10})
D ({1,2,3,5,7})
Explanation opens after your attempt
Correct Answer
A. ({1,4,6,8,9,10})
Step 1
Concept
(P) contains prime numbers up to (10), so the remaining elements are in the complement. (1) is not prime and will be in the complement.
Step 2
Why this answer is correct
The correct answer is A. ({1,4,6,8,9,10}). (P) contains prime numbers up to (10), so the remaining elements are in the complement. (1) is not prime and will be in the complement.
Step 3
Exam Tip
(P) में (10) तक की अभाज्य संख्याएं हैं, इसलिए बाकी अवयव पूरक हैं। (1) अभाज्य नहीं है और पूरक में आएगा।
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यदि \(U={x:x\in \mathbb{N},x\le 9}\) और \(S=\{1,4,9\}\) है, तो (S') क्या होगा?
If \(U={x:x\in \mathbb{N},x\le 9}\) and \(S=\{1,4,9\}\), what will (S') be?
#sets
#squares
#complement
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A ({2,3,5,6,7,8})
B ({1,4,9})
C ({2,3,4,5,6,7,8})
D ({1,2,3,5,6,7,8})
Explanation opens after your attempt
Correct Answer
A. ({2,3,5,6,7,8})
Step 1
Concept
(S) has (1,4,9), so the remaining elements of (U), (2,3,5,6,7,8), are in the complement. Writing \(U={1,2,\ldots,9}\) first helps.
Step 2
Why this answer is correct
The correct answer is A. ({2,3,5,6,7,8}). (S) has (1,4,9), so the remaining elements of (U), (2,3,5,6,7,8), are in the complement. Writing \(U={1,2,\ldots,9}\) first helps.
Step 3
Exam Tip
(S) में (1,4,9) हैं, इसलिए (U) के बाकी (2,3,5,6,7,8) पूरक हैं। पहले \(U={1,2,\ldots,9}\) लिखना सहायक है।
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\(यदि (U={\)red,blue,green,yellow\(}) और (C={\)red,green}) है, तो (C') क्या है?
\(If (U={\)red,blue,green,yellow\(}) and (C={\)red,green}), what is (C')?
#sets
#word_set
#complement
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A ({blue,yellow})
B ({red,green})
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({blue,yellow})
Step 1
Concept
(C') contains colors that are in (U) but not in (C). The same rule applies to sets with words.
Step 2
Why this answer is correct
The correct answer is A. ({blue,yellow}). (C') contains colors that are in (U) but not in (C). The same rule applies to sets with words.
Step 3
Exam Tip
(C') में वे रंग आएंगे जो (U) में हैं पर (C) में नहीं हैं। शब्दों वाले समुच्चयों में भी वही नियम लागू होता है।
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यदि \(U={x:x\in \mathbb{N},x\le 15}\) और \(M=\{5,10,15\}\) है, तो (M') में कितने अवयव होंगे?
If \(U={x:x\in \mathbb{N},x\le 15}\) and \(M=\{5,10,15\}\), how many elements will be in (M')?
#sets
#multiples
#cardinality
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A (12)
B (3)
C (15)
D (10)
Explanation opens after your attempt
Step 1
Concept
(n(U)=15) and (n(M)=3), so (n(M')=12). For the number of complement elements, subtract selected elements from the total.
Step 2
Why this answer is correct
The correct answer is A. (12). (n(U)=15) and (n(M)=3), so (n(M')=12). For the number of complement elements, subtract selected elements from the total.
Step 3
Exam Tip
(n(U)=15) और (n(M)=3), इसलिए (n(M')=12)। पूरक की संख्या के लिए कुल में से चुने गए अवयव घटाएं।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\) और \(A=\{1,2,7,8\}\) है, तो \(A'\cup A\) कौन सा है?
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{1,2,7,8\}\), which is \(A'\cup A\)?
#sets
#union_property
#application
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? Hint Small clue
A ({1,2,3,4,5,6,7,8})
B ({3,4,5,6})
C ({1,2,7,8})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4,5,6,7,8})
Step 1
Concept
\(A'\cup A=U\), so the answer is the whole universal set. Identify (U) in list form among the options.
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4,5,6,7,8}). \(A'\cup A=U\), so the answer is the whole universal set. Identify (U) in list form among the options.
Step 3
Exam Tip
\(A'\cup A=U\), इसलिए उत्तर पूरा सार्वत्रिक समुच्चय है। विकल्पों में (U) को सूची रूप में पहचानें।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\) और \(A=\{3,4,5,6\}\) है, तो \(A'\cap A\) कौन सा है?
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{3,4,5,6\}\), which is \(A'\cap A\)?
#sets
#disjoint
#intersection
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A \(\varnothing\)
B ({1,2,7,8})
C (U)
D (A)
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\)
Step 1
Concept
(A) and (A') are disjoint, so their intersection is \(\varnothing\). No element of (A) remains in its complement.
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). (A) and (A') are disjoint, so their intersection is \(\varnothing\). No element of (A) remains in its complement.
Step 3
Exam Tip
(A) और (A') असंयुक्त होते हैं, इसलिए उनका प्रतिच्छेद \(\varnothing\) है। पूरक में (A) का कोई अवयव नहीं रहता।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,3,4,5\}\) और \(B=\{4,5,6,7\}\) है, तो (\(A\cup B\)') क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,3,4,5\}\), and \(B=\{4,5,6,7\}\), what will (\(A\cup B\)') be?
#sets
#union_complement
#numerical
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A ({8,9})
B ({1,2,3})
C ({6,7,8,9})
D ({4,5})
Explanation opens after your attempt
Correct Answer
A. ({8,9})
Step 1
Concept
\(A\cup B={1,2,3,4,5,6,7}\), so the complement is ({8,9}). First form the union of all included elements.
Step 2
Why this answer is correct
The correct answer is A. ({8,9}). \(A\cup B={1,2,3,4,5,6,7}\), so the complement is ({8,9}). First form the union of all included elements.
Step 3
Exam Tip
\(A\cup B={1,2,3,4,5,6,7}\), इसलिए पूरक ({8,9}) है। पहले सभी शामिल अवयवों का संघ बनाएं।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,3,5,7,9\}\) और \(B=\{2,3,5,8\}\) है, तो (\(A\cap B\)') क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,3,5,7,9\}\), and \(B=\{2,3,5,8\}\), what is (\(A\cap B\)')?
#sets
#intersection_complement
#numerical
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A ({1,2,4,6,7,8,9})
B ({3,5})
C ({1,7,9})
D ({2,4,6,8})
Explanation opens after your attempt
Correct Answer
A. ({1,2,4,6,7,8,9})
Step 1
Concept
\(A\cap B={3,5}\), so removing these from (U) gives the complement. Finding the intersection first is necessary.
Step 2
Why this answer is correct
The correct answer is A. ({1,2,4,6,7,8,9}). \(A\cap B={3,5}\), so removing these from (U) gives the complement. Finding the intersection first is necessary.
Step 3
Exam Tip
\(A\cap B={3,5}\), इसलिए (U) से इन्हें हटाने पर पूरक मिलता है। पहले प्रतिच्छेद निकालना जरूरी है।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(A=\{2,4\}\) है, तो (A'-A) क्या होगा?
If \(U=\{1,2,3,4,5,6\}\) and \(A=\{2,4\}\), what will (A'-A) be?
#sets
#difference
#complement
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A ({1,3,5,6})
B ({2,4})
C \(\varnothing\)
D (U)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,6})
Step 1
Concept
(A') has no element of (A), so (A'-A=A'). First find (A'={1,3,5,6}).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,6}). (A') has no element of (A), so (A'-A=A'). First find (A'={1,3,5,6}).
Step 3
Exam Tip
(A') में (A) का कोई अवयव नहीं होता, इसलिए (A'-A=A') है। पहले (A'={1,3,5,6}) निकालें।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(A=\{1,5,6\}\) है, तो (A-A') क्या होगा?
If \(U=\{1,2,3,4,5,6\}\) and \(A=\{1,5,6\}\), what will (A-A') be?
#sets
#difference
#disjoint
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A ({1,5,6})
B \({2,3,4})
C \(\varnothing\)
D (U)
Explanation opens after your attempt
Correct Answer
A. ({1,5,6})
Step 1
Concept
(A') has no element of (A), so (A-A'=A). Use the disjointness of a set and its complement.
Step 2
Why this answer is correct
The correct answer is A. ({1,5,6}). (A') has no element of (A), so (A-A'=A). Use the disjointness of a set and its complement.
Step 3
Exam Tip
(A') में (A) का कोई अवयव नहीं होता, इसलिए (A-A'=A) है। पूरक असंयुक्तता का उपयोग करें।
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\(यदि (U={1,2,3,4,5,6,7,8,9,10}) और (A={x:x\in U,x\) is a multiple of 2}) है, तो (A') क्या है?
\(If (U={1,2,3,4,5,6,7,8,9,10}) and (A={x:x\in U,x\) is a multiple of 2}), what is (A')?
#sets
#multiples
#complement
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A ({1,3,5,7,9})
B ({2,4,6,8,10})
C ({1,2,3,4,5})
D \({6,7,8,9,10})
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,7,9})
Step 1
Concept
(A) contains multiples of (2), so the complement contains non-multiples (1,3,5,7,9). Apply the condition only inside (U).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,7,9}). (A) contains multiples of (2), so the complement contains non-multiples (1,3,5,7,9). Apply the condition only inside (U).
Step 3
Exam Tip
(A) में (2) के गुणज हैं, इसलिए पूरक में गैर-गुणज (1,3,5,7,9) होंगे। शर्त को (U) के अंदर ही लागू करें।
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यदि \(U={x:x\in \mathbb{N},1\le x\le 20}\) और \(A={x:x\in U,x>12}\) है, तो (n(A')) कितना है?
If \(U={x:x\in \mathbb{N},1\le x\le 20}\) and \(A={x:x\in U,x>12}\), what is (n(A'))?
#sets
#cardinality
#inequality
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A (12)
B (8)
C (20)
D (13)
Explanation opens after your attempt
Step 1
Concept
\(A={13,14,\ldots,20}\) has (8) elements, so (A') has (12) elements. (x>12) does not include (12).
Step 2
Why this answer is correct
The correct answer is A. (12). \(A={13,14,\ldots,20}\) has (8) elements, so (A') has (12) elements. (x>12) does not include (12).
Step 3
Exam Tip
\(A={13,14,\ldots,20}\) में (8) अवयव हैं, इसलिए (A') में (12) अवयव होंगे। (x>12) में (12) शामिल नहीं है।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3\}\) और \(B=\{4,5\}\) है, तो (\(A\cup B\)') में कितने अवयव हैं?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3\}\), and \(B=\{4,5\}\), how many elements are in (\(A\cup B\)')?
#sets
#union_complement
#cardinality
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A (3)
B (5)
C (2)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B={1,2,3,4,5}\), so its complement ({6,7,8}) has (3) elements. First count the union.
Step 2
Why this answer is correct
The correct answer is A. (3). \(A\cup B={1,2,3,4,5}\), so its complement ({6,7,8}) has (3) elements. First count the union.
Step 3
Exam Tip
\(A\cup B={1,2,3,4,5}\), इसलिए पूरक ({6,7,8}) में (3) अवयव हैं। पहले संघ की संख्या देखें।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6\}\) है, तो (\(A\cap B\)') में कितने अवयव हैं?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4\}\), and \(B=\{3,4,5,6\}\), how many elements are in (\(A\cap B\)')?
#sets
#intersection_complement
#cardinality
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A (8)
B (2)
C (6)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(A\cap B={3,4}\), so the complement has (10-2=8) elements. Subtract the size of the intersection from the total.
Step 2
Why this answer is correct
The correct answer is A. (8). \(A\cap B={3,4}\), so the complement has (10-2=8) elements. Subtract the size of the intersection from the total.
Step 3
Exam Tip
\(A\cap B={3,4}\), इसलिए पूरक में (10-2=8) अवयव होंगे। प्रतिच्छेद की संख्या कुल से घटाएं।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(A=\{1,3,5\}\) है, तो कौन सा अवयव (A') में होगा?
If \(U=\{1,2,3,4,5,6\}\) and \(A=\{1,3,5\}\), which element will be in (A')?
#sets
#element_check
#complement
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A (2)
B (1)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
(A') contains elements outside (A), namely (2,4,6). Among the options, only (2) fits.
Step 2
Why this answer is correct
The correct answer is A. (2). (A') contains elements outside (A), namely (2,4,6). Among the options, only (2) fits.
Step 3
Exam Tip
(A') में (A) के बाहर के अवयव (2,4,6) होंगे। दिए गए विकल्पों में केवल (2) ऐसा है।
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यदि \(U=\{m,n,o,p,q\}\) और \(A=\{n,p\}\) है, तो कौन सा अवयव (A') में नहीं होगा?
If \(U=\{m,n,o,p,q\}\) and \(A=\{n,p\}\), which element will not be in (A')?
#sets
#element_check
#common_mistake
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A (n)
B (m)
C (o)
D (q)
Explanation opens after your attempt
Step 1
Concept
Elements of (A) do not appear in (A'), so (n) will not be in (A'). In such questions, read the word not carefully.
Step 2
Why this answer is correct
The correct answer is A. (n). Elements of (A) do not appear in (A'), so (n) will not be in (A'). In such questions, read the word not carefully.
Step 3
Exam Tip
(A') में (A) के अवयव नहीं आते, इसलिए (n) (A') में नहीं होगा। ऐसे प्रश्नों में नहीं शब्द को ध्यान से पढ़ें।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\) और \(A={x:x\in U,x\le 4}\) है, तो (A') का सबसे सही रूप कौन सा है?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A={x:x\in U,x\le 4}\), which is the most correct form of (A')?
#sets
#set_builder
#inequality_complement
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A \(A'={x:x\in U,x>4}\)
B \(A'={x:x\in U,x<4}\)
C \(A'={x:x\in U,x\le 4}\)
D (A'=U)
Explanation opens after your attempt
Correct Answer
A. \(A'={x:x\in U,x>4}\)
Step 1
Concept
(A) contains elements up to (4), so the complement contains elements greater than (4). When reversing the inequality, equality is removed.
Step 2
Why this answer is correct
The correct answer is A. \(A'={x:x\in U,x>4}\). (A) contains elements up to (4), so the complement contains elements greater than (4). When reversing the inequality, equality is removed.
Step 3
Exam Tip
(A) में (4) तक के अवयव हैं, इसलिए पूरक में (4) से बड़े अवयव होंगे। असमानता का उल्टा करते समय बराबरी हटती है।
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