यदि \(A={x\in\mathbb{Z}:-4\le x\le 6}\), \(B={x\in\mathbb{Z}:x^2\le16}\) और \(C={x\in\mathbb{Z}:2\mid x}\) हैं, तो (\(A\cap B\)-C) क्या है?
If \(A={x\in\mathbb{Z}:-4\le x\le 6}\), \(B={x\in\mathbb{Z}:x^2\le16}\), and \(C={x\in\mathbb{Z}:2\mid x}\), what is (\(A\cap B\)-C)?
#sets
#intersection
#difference
#integers
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A ({-3,-1,1,3})
B ({-4,-2,0,2,4})
C ({-3,-2,-1,0,1,2,3})
D ({1,3,5})
Explanation opens after your attempt
Correct Answer
A. ({-3,-1,1,3})
Step 1
Concept
\(A\cap B={-4,-3,-2,-1,0,1,2,3,4}\), and the even elements of (C) are removed. Hence the remaining odd elements are ({-3,-1,1,3}).
Step 2
Why this answer is correct
The correct answer is A. ({-3,-1,1,3}). \(A\cap B={-4,-3,-2,-1,0,1,2,3,4}\), and the even elements of (C) are removed. Hence the remaining odd elements are ({-3,-1,1,3}).
Step 3
Exam Tip
\(A\cap B={-4,-3,-2,-1,0,1,2,3,4}\) है और (C) के सम तत्व हटते हैं। इसलिए विषम तत्व ({-3,-1,1,3}) बचते हैं।
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यदि \(A={x\in\mathbb{Z}: -7\le x\le 7}\), \(B={x\in\mathbb{Z}: x^2\le 16}\) और \(C={x\in\mathbb{Z}: 3\mid x}\) हैं, तो \((A-B)\cap C\) क्या है?
If \(A={x\in\mathbb{Z}: -7\le x\le 7}\), \(B={x\in\mathbb{Z}: x^2\le 16}\), and \(C={x\in\mathbb{Z}: 3\mid x}\), what is \((A-B)\cap C\)?
#sets
#integers
#difference
#intersection
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A ({-6,6})
B ({-3,0,3})
C ({-7,-6,6,7})
D ({-6,-3,0,3,6})
Explanation opens after your attempt
Correct Answer
A. ({-6,6})
Step 1
Concept
\(B=\{-4,-3,-2,-1,0,1,2,3,4\}\), so (A-B={-7,-6,-5,5,6,7}). The elements divisible by (3) are ({-6,6}).
Step 2
Why this answer is correct
The correct answer is A. ({-6,6}). \(B=\{-4,-3,-2,-1,0,1,2,3,4\}\), so (A-B={-7,-6,-5,5,6,7}). The elements divisible by (3) are ({-6,6}).
Step 3
Exam Tip
\(B=\{-4,-3,-2,-1,0,1,2,3,4\}\) है, इसलिए (A-B={-7,-6,-5,5,6,7}) होगा। इनमें (3) से विभाज्य तत्व ({-6,6}) हैं।
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यदि \(A\cup B={2,4,6,8,10,12,14}\), (A-B={2,10}) और (B-A={6,14}) है, तो \(A\cap B\) क्या है?
If \(A\cup B={2,4,6,8,10,12,14}\), (A-B={2,10}), and (B-A={6,14}), what is \(A\cap B\)?
#sets
#venn
#union
#intersection
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A ({4,8,12})
B ({2,10})
C ({6,14})
D ({2,4,6,8,10,12,14})
Explanation opens after your attempt
Correct Answer
A. ({4,8,12})
Step 1
Concept
The union is made of three disjoint parts (A-B), \(A\cap B\), and (B-A). Removing the given only-parts leaves ({4,8,12}).
Step 2
Why this answer is correct
The correct answer is A. ({4,8,12}). The union is made of three disjoint parts (A-B), \(A\cap B\), and (B-A). Removing the given only-parts leaves ({4,8,12}).
Step 3
Exam Tip
संघ तीन अलग भागों (A-B), \(A\cap B\) और (B-A) से बनता है। दिए गए केवल वाले भाग हटाने पर ({4,8,12}) बचता है।
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यदि \(A={x\in\mathbb{R}: -3\le x<5}\), \(B={x\in\mathbb{R}: 1<x\le 8}\) और \(C={x\in\mathbb{R}: x\le 2}\) हैं, तो (\(A\cup B\)\cap C) क्या है?
If \(A={x\in\mathbb{R}: -3\le x<5}\), \(B={x\in\mathbb{R}: 1<x\le 8}\), and \(C={x\in\mathbb{R}: x\le 2}\), what is (\(A\cup B\)\cap C)?
#sets
#intervals
#union
#intersection
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A ([-3,2])
B ((-3,2])
C ([-3,8])
D ((1,2])
Explanation opens after your attempt
Correct Answer
A. ([-3,2])
Step 1
Concept
\(A\cup B=[-3,8]\). Intersecting it with \(x\le 2\) gives ([-3,2]).
Step 2
Why this answer is correct
The correct answer is A. ([-3,2]). \(A\cup B=[-3,8]\). Intersecting it with \(x\le 2\) gives ([-3,2]).
Step 3
Exam Tip
\(A\cup B=[-3,8]\) है। अब \(x\le 2\) से प्रतिच्छेद लेने पर ([-3,2]) मिलता है।
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यदि (n(A)=58), (n(B)=44), (n(A-B)=23) है, तो (n\(A\cup B\)) क्या होगा?
If (n(A)=58), (n(B)=44), and (n(A-B)=23), what is (n\(A\cup B\))?
#sets
#cardinality
#difference
#union
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A (,67,)
B (,79,)
C (,102,)
D (,35,)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cap B\)=58-23=35). Therefore (n\(A\cup B\)=58+44-35=67).
Step 2
Why this answer is correct
The correct answer is A. (,67,). (n\(A\cap B\)=58-23=35). Therefore (n\(A\cup B\)=58+44-35=67).
Step 3
Exam Tip
(n\(A\cap B\)=58-23=35) है। इसलिए (n\(A\cup B\)=58+44-35=67)।
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यदि (n(A)=64), (n(B)=57), (n\(A\cap B\)=29) और (n(U)=110) है, तो (n(\(A\cup B\)')) कितना है?
If (n(A)=64), (n(B)=57), (n\(A\cap B\)=29), and (n(U)=110), what is (n(\(A\cup B\)'))?
#sets
#cardinality
#union
#complement
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A (,18,)
B (,92,)
C (,29,)
D (,46,)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\)=64+57-29=92). Therefore (n(\(A\cup B\)')=110-92=18).
Step 2
Why this answer is correct
The correct answer is A. (,18,). (n\(A\cup B\)=64+57-29=92). Therefore (n(\(A\cup B\)')=110-92=18).
Step 3
Exam Tip
(n\(A\cup B\)=64+57-29=92) है। इसलिए (n(\(A\cup B\)')=110-92=18)।
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यदि \(A={x\in\mathbb{R}:x^2-5x+6\le0}\) और \(B={x\in\mathbb{R}:x<4}\), तो (A-B) क्या है?
If \(A={x\in\mathbb{R}:x^2-5x+6\le0}\) and \(B={x\in\mathbb{R}:x<4}\), what is (A-B)?
#sets
#intervals
#quadratic-inequality
#difference
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A \(\varnothing\)
B ([2,3])
C ([3,4))
D \([4,\infty\))
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\)
Step 1
Concept
\(x^2-5x+6\le0\) gives (A=[2,3]). Every element of (A) lies in (B), so \(A-B=\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). \(x^2-5x+6\le0\) gives (A=[2,3]). Every element of (A) lies in (B), so \(A-B=\varnothing\).
Step 3
Exam Tip
\(x^2-5x+6\le0\) से (A=[2,3]) मिलता है। (A) का हर तत्व (B) में है, इसलिए \(A-B=\varnothing\)।
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यदि \(A\subseteq B\) और \(C\cap B=\varnothing\) है, तो (\(A\cup C\)\cap B) किसके बराबर है?
If \(A\subseteq B\) and \(C\cap B=\varnothing\), then (\(A\cup C\)\cap B) is equal to which set?
#sets
#subset
#union
#intersection
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A (A)
B (B)
C (C)
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Since \(A\subseteq B\), all of (A) lies in (B), and (C) has no common element with (B). Hence only (A) remains in the intersection.
Step 2
Why this answer is correct
The correct answer is A. (A). Since \(A\subseteq B\), all of (A) lies in (B), and (C) has no common element with (B). Hence only (A) remains in the intersection.
Step 3
Exam Tip
\(A\subseteq B\) होने से (A) का पूरा भाग (B) में रहता है और (C) का (B) से कोई सामान्य तत्व नहीं है। इसलिए प्रतिच्छेद में केवल (A) बचेगा।
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यदि \(A={x\in\mathbb{R}:|x-2|\le3}\) और \(B={x\in\mathbb{R}:x^2\le4}\), तो \(A\cap B\) क्या है?
If \(A={x\in\mathbb{R}:|x-2|\le3}\) and \(B={x\in\mathbb{R}:x^2\le4}\), what is \(A\cap B\)?
#sets
#absolute-value
#intersection
#intervals
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A ([-1,2])
B ([-2,2])
C ([-1,5])
D ((2,5])
Explanation opens after your attempt
Correct Answer
A. ([-1,2])
Step 1
Concept
(A=[-1,5]) and (B=[-2,2]). Their common part is ([-1,2]).
Step 2
Why this answer is correct
The correct answer is A. ([-1,2]). (A=[-1,5]) and (B=[-2,2]). Their common part is ([-1,2]).
Step 3
Exam Tip
(A=[-1,5]) और (B=[-2,2]) है। दोनों का समान भाग ([-1,2]) है।
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यदि \(A\subseteq U\), \(B\subseteq U\) और \(A-B=A\cap B'\) है, तो ((A-B)\cup\(A\cap B\)) किसके बराबर है?
If \(A\subseteq U\), \(B\subseteq U\), and \(A-B=A\cap B'\), then ((A-B)\cup\(A\cap B\)) is equal to which set?
#sets
#identity
#difference
#intersection
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A (A)
B (B)
C \(A\cup B\)
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
(A-B) and \(A\cap B\) are two disjoint parts of (A). Their union gives the whole set (A).
Step 2
Why this answer is correct
The correct answer is A. (A). (A-B) and \(A\cap B\) are two disjoint parts of (A). Their union gives the whole set (A).
Step 3
Exam Tip
(A-B) और \(A\cap B\), (A) के दो अलग भाग हैं। इनके संघ से पूरा (A) मिल जाता है।
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यदि \(A=\{1,2,3,4,5,6,7\}\), \(B=\{2,4,6,8\}\) और \(C=\{1,4,7,8\}\), तो (\(A\cup B\)\cap C) क्या है?
If \(A=\{1,2,3,4,5,6,7\}\), \(B=\{2,4,6,8\}\), and \(C=\{1,4,7,8\}\), what is (\(A\cup B\)\cap C)?
#sets
#union
#intersection
#three-sets
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A ({1,4,7,8})
B ({1,4,7})
C ({4,8})
D ({2,4,6})
Explanation opens after your attempt
Correct Answer
A. ({1,4,7,8})
Step 1
Concept
\(A\cup B={1,2,3,4,5,6,7,8}\). Its intersection with (C) gives the whole \(C=\{1,4,7,8\}\).
Step 2
Why this answer is correct
The correct answer is A. ({1,4,7,8}). \(A\cup B={1,2,3,4,5,6,7,8}\). Its intersection with (C) gives the whole \(C=\{1,4,7,8\}\).
Step 3
Exam Tip
\(A\cup B={1,2,3,4,5,6,7,8}\) है। इसका (C) से प्रतिच्छेद पूरा \(C=\{1,4,7,8\}\) देता है।
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यदि (A-B={p,q}), \(A\cap B={r,s,t}\) और (B-A={u}), तो (n(A)) कितना है?
If (A-B={p,q}), \(A\cap B={r,s,t}\), and (B-A={u}), what is (n(A))?
#sets
#cardinality
#venn
#difference
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A (,5,)
B (,3,)
C (,6,)
D (,2,)
Explanation opens after your attempt
Step 1
Concept
Set (A) contains the elements of (A-B) and \(A\cap B\). Hence (n(A)=2+3=5).
Step 2
Why this answer is correct
The correct answer is A. (,5,). Set (A) contains the elements of (A-B) and \(A\cap B\). Hence (n(A)=2+3=5).
Step 3
Exam Tip
समुच्चय (A) में (A-B) और \(A\cap B\) के तत्व आते हैं। इसलिए (n(A)=2+3=5)।
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यदि \(A\cap B=\varnothing\) और \(A\cup B=A\cup C\) है, तो \(B\subseteq C\) होने के लिए कौन-सी अतिरिक्त शर्त पर्याप्त है?
If \(A\cap B=\varnothing\) and \(A\cup B=A\cup C\), which additional condition is sufficient for \(B\subseteq C\)?
#sets
#reasoning
#union
#disjoint
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A \(A\cap C=\varnothing\)
B \(A\subseteq C\)
C \(B\cap C=\varnothing\)
D \(C\subseteq A\)
Explanation opens after your attempt
Correct Answer
A. \(A\cap C=\varnothing\)
Step 1
Concept
If \(A\cap C=\varnothing\), then the part outside (A) must match in the equal unions. Hence \(B\subseteq C\).
Step 2
Why this answer is correct
The correct answer is A. \(A\cap C=\varnothing\). If \(A\cap C=\varnothing\), then the part outside (A) must match in the equal unions. Hence \(B\subseteq C\).
Step 3
Exam Tip
यदि \(A\cap C=\varnothing\), तो संघ की समानता में (A) से बाहर वाला भाग समान होना चाहिए। इसलिए \(B\subseteq C\) मिलता है।
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यदि \(A={x\in\mathbb{N}:x\le40,\ 4\mid x}\) और \(B={x\in\mathbb{N}:x\le40,\ 6\mid x}\), तो \(A\cap B\) क्या है?
If \(A={x\in\mathbb{N}:x\le40,\ 4\mid x}\) and \(B={x\in\mathbb{N}:x\le40,\ 6\mid x}\), what is \(A\cap B\)?
#sets
#multiples
#intersection
#lcm
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A ({12,24,36})
B \({4,8,12,\ldots,40}\)
C \({6,12,18,\ldots,36}\)
D ({2,12,24,36})
Explanation opens after your attempt
Correct Answer
A. ({12,24,36})
Step 1
Concept
A number divisible by both (4) and (6) is divisible by (\operatorname{lcm}(4,6)=12). Up to (40), the multiples are ({12,24,36}).
Step 2
Why this answer is correct
The correct answer is A. ({12,24,36}). A number divisible by both (4) and (6) is divisible by (\operatorname{lcm}(4,6)=12). Up to (40), the multiples are ({12,24,36}).
Step 3
Exam Tip
जो संख्या (4) और (6) दोनों से विभाज्य है, वह (\operatorname{lcm}(4,6)=12) से विभाज्य होगी। (40) तक ऐसे गुणज ({12,24,36}) हैं।
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यदि \(A={x\in\mathbb{N}:x\mid 72}\) और \(B={x\in\mathbb{N}:x\mid 90}\), तो \(A\cap B\) क्या है?
If \(A={x\in\mathbb{N}:x\mid 72}\) and \(B={x\in\mathbb{N}:x\mid 90}\), what is \(A\cap B\)?
#sets
#divisors
#intersection
#gcd
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A ({1,2,3,6,9,18})
B ({1,2,3,5,6,9,10,15,18,30,45,90})
C ({18})
D ({1,2,4,8,9,18,36,72})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,6,9,18})
Step 1
Concept
Common divisors are divisors of (\gcd(72,90)=18). Thus \(A\cap B={1,2,3,6,9,18}\).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,6,9,18}). Common divisors are divisors of (\gcd(72,90)=18). Thus \(A\cap B={1,2,3,6,9,18}\).
Step 3
Exam Tip
सामान्य भाजक (\gcd(72,90)=18) के भाजक होंगे। अतः \(A\cap B={1,2,3,6,9,18}\)।
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यदि \(A=\{1,2,3,4,5\}\), \(B=\{3,4,5,6\}\) और \(C=\{5,6,7\}\), तो \((A-B)\cup(B-C)\) क्या है?
If \(A=\{1,2,3,4,5\}\), \(B=\{3,4,5,6\}\), and \(C=\{5,6,7\}\), what is \((A-B)\cup(B-C)\)?
#sets
#difference
#union
#three-sets
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A ({1,2,3,4})
B ({1,2})
C ({3,4})
D ({5,6})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4})
Step 1
Concept
(A-B={1,2}) and (B-C={3,4}). Their union is ({1,2,3,4}).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4}). (A-B={1,2}) and (B-C={3,4}). Their union is ({1,2,3,4}).
Step 3
Exam Tip
(A-B={1,2}) और (B-C={3,4}) है। इनका संघ ({1,2,3,4}) है।
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कौन-सा विकल्प (\(A\cup B\)-A) के बराबर है?
Which option is equal to (\(A\cup B\)-A)?
#sets
#identity
#union
#difference
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A (B-A)
B (A-B)
C \(A\cap B\)
D \(A\cup B\)
Explanation opens after your attempt
Step 1
Concept
Removing (A) from the union leaves only the elements that are in (B) but not in (A). Hence the result is (B-A).
Step 2
Why this answer is correct
The correct answer is A. (B-A). Removing (A) from the union leaves only the elements that are in (B) but not in (A). Hence the result is (B-A).
Step 3
Exam Tip
संघ से (A) हटाने पर केवल वे तत्व बचते हैं जो (B) में हैं पर (A) में नहीं। इसलिए परिणाम (B-A) है।
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यदि \(A\cap B=A\) और \(B\cap C=B\) हैं, तो कौन-सा निष्कर्ष सही है?
If \(A\cap B=A\) and \(B\cap C=B\), which conclusion is correct?
#sets
#subset
#intersection
#reasoning
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A \(A\subseteq C\)
B \(C\subseteq A\)
C (A=C)
D \(A\cap C=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(A\subseteq C\)
Step 1
Concept
\(A\cap B=A\) gives \(A\subseteq B\), and \(B\cap C=B\) gives \(B\subseteq C\). Therefore \(A\subseteq C\).
Step 2
Why this answer is correct
The correct answer is A. \(A\subseteq C\). \(A\cap B=A\) gives \(A\subseteq B\), and \(B\cap C=B\) gives \(B\subseteq C\). Therefore \(A\subseteq C\).
Step 3
Exam Tip
\(A\cap B=A\) से \(A\subseteq B\) और \(B\cap C=B\) से \(B\subseteq C\) मिलता है। इसलिए \(A\subseteq C\)।
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यदि \(A={x\in\mathbb{Z}:x^2-1=0}\) और \(B={x\in\mathbb{Z}:x^2=1}\), तो (A-B) क्या है?
If \(A={x\in\mathbb{Z}:x^2-1=0}\) and \(B={x\in\mathbb{Z}:x^2=1}\), what is (A-B)?
#sets
#equal-sets
#difference
#integers
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A \(\varnothing\)
B ({-1,1})
C ({0})
D ({-1})
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\)
Step 1
Concept
Both conditions give the same set ({-1,1}). The difference of equal sets is the empty set.
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). Both conditions give the same set ({-1,1}). The difference of equal sets is the empty set.
Step 3
Exam Tip
दोनों शर्तों से वही समुच्चय ({-1,1}) मिलता है। समान समुच्चयों का अंतर खाली समुच्चय होता है।
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यदि (n\(A\cup B\)=96), (n\(A\cap B\)=18) और (n(A-B)=41) है, तो (n(B)) कितना है?
If (n\(A\cup B\)=96), (n\(A\cap B\)=18), and (n(A-B)=41), what is (n(B))?
#sets
#cardinality
#venn
#union
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A (,55,)
B (,37,)
C (,73,)
D (,78,)
Explanation opens after your attempt
Step 1
Concept
The sum of (A-B), \(A\cap B\), and (B-A) is (96), so (B-A=96-41-18=37). Thus (n(B)=37+18=55).
Step 2
Why this answer is correct
The correct answer is A. (,55,). The sum of (A-B), \(A\cap B\), and (B-A) is (96), so (B-A=96-41-18=37). Thus (n(B)=37+18=55).
Step 3
Exam Tip
(A-B), \(A\cap B\) और (B-A) का योग (96) है, इसलिए (B-A=96-41-18=37)। अतः (n(B)=37+18=55)।
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यदि \(A={x:x\) अंग्रेजी शब्द (ALGEBRA) का अक्षर है(}) और \(B={x:x\) अंग्रेजी शब्द (GEOMETRY) का अक्षर है(}), तो \(A\cup B\) क्या है?
If \(A={x:x\) is a letter of the English word (ALGEBRA)(}) and \(B={x:x\) is a letter of the English word (GEOMETRY)(}), what is \(A\cup B\)?
#sets
#letters
#union
#roster-form
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A ({A,B,E,G,L,M,O,R,T,Y})
B ({A,B,G,L,R})
C ({E,G,R})
D ({A,E,G,M,O,T,Y})
Explanation opens after your attempt
Correct Answer
A. ({A,B,E,G,L,M,O,R,T,Y})
Step 1
Concept
Repeated letters are written only once in a set. The union of all distinct letters from both words is ({A,B,E,G,L,M,O,R,T,Y}).
Step 2
Why this answer is correct
The correct answer is A. ({A,B,E,G,L,M,O,R,T,Y}). Repeated letters are written only once in a set. The union of all distinct letters from both words is ({A,B,E,G,L,M,O,R,T,Y}).
Step 3
Exam Tip
समुच्चय में दोहराए गए अक्षर एक बार ही लिखे जाते हैं। दोनों शब्दों के सभी अलग अक्षरों का संघ ({A,B,E,G,L,M,O,R,T,Y}) है।
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\(यदि (A={x\in\mathbb{N}:x\le25,\ x\) अभाज्य है\(}) और (B={x\in\mathbb{N}:x\le25,\ x\) विषम है}), तो (B-A) क्या है?
\(If (A={x\in\mathbb{N}:x\le25,\ x\) is prime\(}) and (B={x\in\mathbb{N}:x\le25,\ x\) is odd}), what is (B-A)?
#sets
#prime-numbers
#difference
#number-sets
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A ({1,9,15,21,25})
B ({3,5,7,11,13,17,19,23})
C ({2})
D ({1,3,5,7,9,11,13,15,17,19,21,23,25})
Explanation opens after your attempt
Correct Answer
A. ({1,9,15,21,25})
Step 1
Concept
From the odd numbers in (B), remove the primes in (A). The remaining odd composites and (1) are ({1,9,15,21,25}).
Step 2
Why this answer is correct
The correct answer is A. ({1,9,15,21,25}). From the odd numbers in (B), remove the primes in (A). The remaining odd composites and (1) are ({1,9,15,21,25}).
Step 3
Exam Tip
(B) की विषम संख्याओं में से अभाज्य संख्याएं हटानी हैं। इसलिए बची हुई विषम संयुक्त संख्याएं और (1), अर्थात ({1,9,15,21,25}), मिलती हैं।
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यदि \(U={1,2,\ldots,20}\), \(A={x\in U:2\mid x}\) और \(B={x\in U:5\mid x}\), तो (\(A\cup B\)') क्या है?
If \(U={1,2,\ldots,20}\), \(A={x\in U:2\mid x}\), and \(B={x\in U:5\mid x}\), what is (\(A\cup B\)')?
#sets
#complement
#union
#multiples
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A ({1,3,7,9,11,13,17,19})
B ({2,4,5,6,8,10,12,14,15,16,18,20})
C ({1,3,5,7,9,11,13,15,17,19})
D ({10,20})
Explanation opens after your attempt
Correct Answer
A. ({1,3,7,9,11,13,17,19})
Step 1
Concept
Remove numbers divisible by (2) or (5) from (U). The remaining numbers are ({1,3,7,9,11,13,17,19}).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,7,9,11,13,17,19}). Remove numbers divisible by (2) or (5) from (U). The remaining numbers are ({1,3,7,9,11,13,17,19}).
Step 3
Exam Tip
(2) या (5) से विभाज्य संख्याओं को (U) से हटाते हैं। बची संख्याएं ({1,3,7,9,11,13,17,19}) हैं।
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यदि \(A={x\in\mathbb{R}:x\le1}\) और \(B={x\in\mathbb{R}:x>-2}\), तो \(A\cap B\) क्या है?
If \(A={x\in\mathbb{R}:x\le1}\) and \(B={x\in\mathbb{R}:x>-2}\), what is \(A\cap B\)?
#sets
#intervals
#intersection
#real-numbers
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A ((-2,1])
B ([-2,1])
C (\(-\infty,1]\)
D (\(-2,\infty\))
Explanation opens after your attempt
Correct Answer
A. ((-2,1])
Step 1
Concept
Combining both conditions gives \(-2<x\le1\). Hence the intersection is ((-2,1]).
Step 2
Why this answer is correct
The correct answer is A. ((-2,1]). Combining both conditions gives \(-2<x\le1\). Hence the intersection is ((-2,1]).
Step 3
Exam Tip
दोनों शर्तें साथ रखने पर \(-2<x\le1\) मिलता है। इसलिए प्रतिच्छेद ((-2,1]) है।
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यदि \(A\cup B=B\) और \(A\cap C=C\) हैं, तो कौन-सा कथन अवश्य सत्य है?
If \(A\cup B=B\) and \(A\cap C=C\), which statement must be true?
#sets
#subset
#union
#intersection
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A \(C\subseteq B\)
B \(B\subseteq C\)
C (A=B)
D \(B\cap C=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(C\subseteq B\)
Step 1
Concept
\(A\cup B=B\) gives \(A\subseteq B\), and \(A\cap C=C\) gives \(C\subseteq A\). Therefore \(C\subseteq B\).
Step 2
Why this answer is correct
The correct answer is A. \(C\subseteq B\). \(A\cup B=B\) gives \(A\subseteq B\), and \(A\cap C=C\) gives \(C\subseteq A\). Therefore \(C\subseteq B\).
Step 3
Exam Tip
\(A\cup B=B\) से \(A\subseteq B\) और \(A\cap C=C\) से \(C\subseteq A\) मिलता है। इसलिए \(C\subseteq B\)।
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यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\) और \(C=\{1,3,5\}\), तो \((A-B)\cap C\) क्या है?
If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\), and \(C=\{1,3,5\}\), what is \((A-B)\cap C\)?
#sets
#difference
#intersection
#finite-sets
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A ({1,3,5})
B \(\varnothing\)
C ({2,4,6})
D ({1,2,3,4,5,6})
Explanation opens after your attempt
Correct Answer
A. ({1,3,5})
Step 1
Concept
(A-B={1,3,5}). Its intersection with (C) gives the same set ({1,3,5}).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5}). (A-B={1,3,5}). Its intersection with (C) gives the same set ({1,3,5}).
Step 3
Exam Tip
(A-B={1,3,5}) है। इसका (C) से प्रतिच्छेद वही ({1,3,5}) देता है।
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यदि \(A={x\in\mathbb{Z}: -6\le x\le6}\) और \(B={x\in\mathbb{Z}:x^2<10}\), तो (A-B) क्या है?
If \(A={x\in\mathbb{Z}: -6\le x\le6}\) and \(B={x\in\mathbb{Z}:x^2<10}\), what is (A-B)?
#sets
#integers
#difference
#inequality
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A ({-6,-5,-4,4,5,6})
B ({-3,-2,-1,0,1,2,3})
C ({-6,-5,-4,-3,3,4,5,6})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({-6,-5,-4,4,5,6})
Step 1
Concept
\(B=\{-3,-2,-1,0,1,2,3\}\). Removing it from (A) leaves ({-6,-5,-4,4,5,6}).
Step 2
Why this answer is correct
The correct answer is A. ({-6,-5,-4,4,5,6}). \(B=\{-3,-2,-1,0,1,2,3\}\). Removing it from (A) leaves ({-6,-5,-4,4,5,6}).
Step 3
Exam Tip
\(B=\{-3,-2,-1,0,1,2,3\}\) है। इसे (A) से हटाने पर ({-6,-5,-4,4,5,6}) बचता है।
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यदि \(A\triangle B=(A-B)\cup(B-A)\) और (n\(A\triangle B\)=26), (n\(A\cap B\)=9) है, तो (n\(A\cup B\)) कितना है?
If \(A\triangle B=(A-B)\cup(B-A)\) and (n\(A\triangle B\)=26), (n\(A\cap B\)=9), what is (n\(A\cup B\))?
#sets
#symmetric-difference
#cardinality
#union
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A (,35,)
B (,17,)
C (,26,)
D (,52,)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B\) is made of the disjoint parts symmetric difference and intersection. Hence (n\(A\cup B\)=26+9=35).
Step 2
Why this answer is correct
The correct answer is A. (,35,). \(A\cup B\) is made of the disjoint parts symmetric difference and intersection. Hence (n\(A\cup B\)=26+9=35).
Step 3
Exam Tip
\(A\cup B\) सममित अंतर और प्रतिच्छेद के अलग भागों से बनता है। इसलिए (n\(A\cup B\)=26+9=35)।
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यदि \(A-B=\varnothing\) और \(B-C=\varnothing\) है, तो कौन-सा निष्कर्ष सही है?
If \(A-B=\varnothing\) and \(B-C=\varnothing\), which conclusion is correct?
#sets
#difference
#subset
#reasoning
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A \(A\subseteq C\)
B \(C\subseteq A\)
C (A=C)
D \(A\cap C=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(A\subseteq C\)
Step 1
Concept
\(A-B=\varnothing\) gives \(A\subseteq B\), and \(B-C=\varnothing\) gives \(B\subseteq C\). Therefore \(A\subseteq C\).
Step 2
Why this answer is correct
The correct answer is A. \(A\subseteq C\). \(A-B=\varnothing\) gives \(A\subseteq B\), and \(B-C=\varnothing\) gives \(B\subseteq C\). Therefore \(A\subseteq C\).
Step 3
Exam Tip
\(A-B=\varnothing\) से \(A\subseteq B\) और \(B-C=\varnothing\) से \(B\subseteq C\) मिलता है। इसलिए \(A\subseteq C\)।
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यदि \(A={x\in\mathbb{R}:1\le x\le9}\), \(B={x\in\mathbb{R}:3<x<7}\), तो (A-B) क्या है?
If \(A={x\in\mathbb{R}:1\le x\le9}\), \(B={x\in\mathbb{R}:3<x<7}\), what is (A-B)?
#sets
#intervals
#difference
#endpoints
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A \([1,3]\cup[7,9]\)
B ([1,3)\cup(7,9])
C ((3,7))
D ([1,9])
Explanation opens after your attempt
Correct Answer
A. \([1,3]\cup[7,9]\)
Step 1
Concept
(B) does not include (3) and (7), so they remain in (A-B). The result is \([1,3]\cup[7,9]\).
Step 2
Why this answer is correct
The correct answer is A. \([1,3]\cup[7,9]\). (B) does not include (3) and (7), so they remain in (A-B). The result is \([1,3]\cup[7,9]\).
Step 3
Exam Tip
(B) में (3) और (7) शामिल नहीं हैं, इसलिए वे (A-B) में रहेंगे। परिणाम \([1,3]\cup[7,9]\) है।
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यदि (A) और (B) ऐसे समुच्चय हैं कि \(A\cap B=\varnothing\), तो (\(A\cup B\)-B) क्या है?
If (A) and (B) are sets such that \(A\cap B=\varnothing\), what is (\(A\cup B\)-B)?
#sets
#disjoint
#union
#difference
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A (A)
B (B)
C \(\varnothing\)
D \(A\cap B\)
Explanation opens after your attempt
Step 1
Concept
For disjoint sets, removing (B) from the union leaves only (A). Hence (\(A\cup B\)-B=A).
Step 2
Why this answer is correct
The correct answer is A. (A). For disjoint sets, removing (B) from the union leaves only (A). Hence (\(A\cup B\)-B=A).
Step 3
Exam Tip
असंबद्ध समुच्चयों में (B) हटाने पर संघ से केवल (A) बचता है। इसलिए (\(A\cup B\)-B=A)।
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यदि (n(U)=120), (n(A)=70), (n(B)=65) और (n\(A\cap B\)=40), तो (n\(A'\cap B'\)) क्या है?
If (n(U)=120), (n(A)=70), (n(B)=65), and (n\(A\cap B\)=40), what is (n\(A'\cap B'\))?
#sets
#complement
#cardinality
#de-morgan
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A (,25,)
B (,95,)
C (,15,)
D (,55,)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\)=70+65-40=95). Therefore (n\(A'\cap B'\)=n(\(A\cup B\)')=120-95=25).
Step 2
Why this answer is correct
The correct answer is A. (,25,). (n\(A\cup B\)=70+65-40=95). Therefore (n\(A'\cap B'\)=n(\(A\cup B\)')=120-95=25).
Step 3
Exam Tip
(n\(A\cup B\)=70+65-40=95) है। इसलिए (n\(A'\cap B'\)=n(\(A\cup B\)')=120-95=25)।
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यदि \(A=\{1,2,4,8,16\}\), \(B=\{1,3,9,27\}\) और \(C=\{1,5,25\}\), तो (\(A\cap B\)\cup\(B\cap C\)\cup\(C\cap A\)) क्या है?
If \(A=\{1,2,4,8,16\}\), \(B=\{1,3,9,27\}\), and \(C=\{1,5,25\}\), what is (\(A\cap B\)\cup\(B\cap C\)\cup\(C\cap A\))?
#sets
#pairwise-intersection
#union
#three-sets
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A ({1})
B \(\varnothing\)
C ({1,2,3,5})
D ({2,3,5})
Explanation opens after your attempt
Step 1
Concept
The only common element in each pair of sets is (1). Hence the union of all pairwise intersections is ({1}).
Step 2
Why this answer is correct
The correct answer is A. ({1}). The only common element in each pair of sets is (1). Hence the union of all pairwise intersections is ({1}).
Step 3
Exam Tip
हर दो समुच्चयों का सामान्य तत्व केवल (1) है। इसलिए सभी युग्म प्रतिच्छेदों का संघ ({1}) है।
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यदि \(A={x\in\mathbb{Z}: -3\le x\le8}\), \(B={x\in\mathbb{Z}:0\le x\le5}\) और \(C={x\in\mathbb{Z}:x\) सम है(}), तो \((A-B)\cap C\) क्या है?
If \(A={x\in\mathbb{Z}: -3\le x\le8}\), \(B={x\in\mathbb{Z}:0\le x\le5}\), and \(C={x\in\mathbb{Z}:x\) is even(}), what is \((A-B)\cap C\)?
#sets
#integers
#difference
#intersection
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A ({-2,6,8})
B ({-3,-2,-1,6,7,8})
C ({0,2,4})
D ({-2,0,2,4,6,8})
Explanation opens after your attempt
Correct Answer
A. ({-2,6,8})
Step 1
Concept
(A-B={-3,-2,-1,6,7,8}). The even elements among these are ({-2,6,8}).
Step 2
Why this answer is correct
The correct answer is A. ({-2,6,8}). (A-B={-3,-2,-1,6,7,8}). The even elements among these are ({-2,6,8}).
Step 3
Exam Tip
(A-B={-3,-2,-1,6,7,8}) है। इनमें सम तत्व ({-2,6,8}) हैं।
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यदि \(A={x\in\mathbb{N}:x\le10}\), \(B={x\in\mathbb{N}:x\) विषम है(}) और \(C={x\in\mathbb{N}:x\) अभाज्य है(}), तो \(A\cap(B-C)\) क्या है?
If \(A={x\in\mathbb{N}:x\le10}\), \(B={x\in\mathbb{N}:x\) is odd(}), and \(C={x\in\mathbb{N}:x\) is prime(}), what is \(A\cap(B-C)\)?
#sets
#number-sets
#difference
#intersection
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A ({1,9})
B ({3,5,7})
C ({1,3,5,7,9})
D ({2,4,6,8,10})
Explanation opens after your attempt
Correct Answer
A. ({1,9})
Step 1
Concept
The odd numbers up to (10) are ({1,3,5,7,9}). Removing primes leaves ({1,9}).
Step 2
Why this answer is correct
The correct answer is A. ({1,9}). The odd numbers up to (10) are ({1,3,5,7,9}). Removing primes leaves ({1,9}).
Step 3
Exam Tip
(10) तक की विषम संख्याएं ({1,3,5,7,9}) हैं। इनमें अभाज्य हटाने पर ({1,9}) बचता है।
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यदि \(A\cup B=A\cup C\) और \(A\cap B=A\cap C\), तो निम्न में कौन-सा सही है?
If \(A\cup B=A\cup C\) and \(A\cap B=A\cap C\), which of the following is correct?
#sets
#proof
#union
#intersection
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A (B=C)
B (A=B)
C (A=C)
D \(B\cap C=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
These two equalities make the membership of (B) and (C) the same both inside and outside (A). Hence (B=C).
Step 2
Why this answer is correct
The correct answer is A. (B=C). These two equalities make the membership of (B) and (C) the same both inside and outside (A). Hence (B=C).
Step 3
Exam Tip
इन दोनों समानताओं से (A) के अंदर और बाहर (B) और (C) की सदस्यता समान हो जाती है। अतः (B=C)।
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यदि \(A={x\in\mathbb{R}:x^2-4x+3>0}\) और \(B={x\in\mathbb{R}:x>1}\), तो \(A\cap B\) क्या है?
If \(A={x\in\mathbb{R}:x^2-4x+3>0}\) and \(B={x\in\mathbb{R}:x>1}\), what is \(A\cap B\)?
#sets
#quadratic-inequality
#intersection
#intervals
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A (\(3,\infty\))
B ((1,3))
C (\(-\infty,1\))
D (\(1,\infty\))
Explanation opens after your attempt
Correct Answer
A. (\(3,\infty\))
Step 1
Concept
\(x^2-4x+3>0\) gives (x<1) or (x>3). With (x>1), the common part is (\(3,\infty\)).
Step 2
Why this answer is correct
The correct answer is A. (\(3,\infty\)). \(x^2-4x+3>0\) gives (x<1) or (x>3). With (x>1), the common part is (\(3,\infty\)).
Step 3
Exam Tip
\(x^2-4x+3>0\) से (x<1) या (x>3) मिलता है। (x>1) के साथ सामान्य भाग (\(3,\infty\)) है।
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यदि \(A={x\in\mathbb{R}:x^2\le9}\) और \(B={x\in\mathbb{R}:x^2<1}\), तो (A-B) क्या है?
If \(A={x\in\mathbb{R}:x^2\le9}\) and \(B={x\in\mathbb{R}:x^2<1}\), what is (A-B)?
#sets
#intervals
#difference
#quadratic-inequality
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A \([-3,-1]\cup[1,3]\)
B \((-3,-1)\cup(1,3)\)
C ([-1,1])
D ([-3,3])
Explanation opens after your attempt
Correct Answer
A. \([-3,-1]\cup[1,3]\)
Step 1
Concept
(A=[-3,3]) and (B=(-1,1)). Removing (B) gives \([-3,-1]\cup[1,3]\).
Step 2
Why this answer is correct
The correct answer is A. \([-3,-1]\cup[1,3]\). (A=[-3,3]) and (B=(-1,1)). Removing (B) gives \([-3,-1]\cup[1,3]\).
Step 3
Exam Tip
(A=[-3,3]) और (B=(-1,1)) है। (B) हटाने पर \([-3,-1]\cup[1,3]\) मिलता है।
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यदि \(A=\{1,2,3\}\) और \(B=\{2,3,4,5\}\), तो (\mathcal{P}\(A\cup B\)) में कितने तत्व हैं?
If \(A=\{1,2,3\}\) and \(B=\{2,3,4,5\}\), how many elements are in (\mathcal{P}\(A\cup B\))?
#sets
#power-set
#union
#cardinality
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A (,32,)
B (,16,)
C (,8,)
D (,5,)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B={1,2,3,4,5}\) has (5) elements. Its power set has \(2^5=32\) elements.
Step 2
Why this answer is correct
The correct answer is A. (,32,). \(A\cup B={1,2,3,4,5}\) has (5) elements. Its power set has \(2^5=32\) elements.
Step 3
Exam Tip
\(A\cup B={1,2,3,4,5}\) में (5) तत्व हैं। घात समुच्चय में \(2^5=32\) तत्व होते हैं।
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यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\), तो (n(\mathcal{P}(A-B))) कितना है?
If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\), what is (n(\mathcal{P}(A-B)))?
#sets
#power-set
#difference
#cardinality
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A (,8,)
B (,3,)
C (,6,)
D (,16,)
Explanation opens after your attempt
Step 1
Concept
(A-B={1,3,5}) has (3) elements. Therefore (n(\mathcal{P}(A-B))=23 =8).
Step 2
Why this answer is correct
The correct answer is A. (,8,). (A-B={1,3,5}) has (3) elements. Therefore (n(\mathcal{P}(A-B))=23 =8).
Step 3
Exam Tip
(A-B={1,3,5}) में (3) तत्व हैं। इसलिए (n(\mathcal{P}(A-B))=23 =8)।
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यदि (n(A-B)=17), (n(B-C)=22), और (B-C) में (A) के साथ (6) सामान्य तत्व हैं, तो (n\((A-B)\cup(B-C)\)) क्या है?
If (n(A-B)=17), (n(B-C)=22), and (B-C) has (6) elements common with (A), what is (n\((A-B)\cup(B-C)\))?
#sets
#cardinality
#union
#difference
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A (,33,)
B (,39,)
C (,45,)
D (,28,)
Explanation opens after your attempt
Step 1
Concept
\((A-B)\cap(B-C)\) contains those (6) elements common to (B-C) and (A). Hence the union count is (17+22-6=33).
Step 2
Why this answer is correct
The correct answer is A. (,33,). \((A-B)\cap(B-C)\) contains those (6) elements common to (B-C) and (A). Hence the union count is (17+22-6=33).
Step 3
Exam Tip
\((A-B)\cap(B-C)\) में वही (6) तत्व हैं जो (B-C) में (A) के साथ सामान्य हैं। इसलिए संघ का मान (17+22-6=33) है।
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यदि (A), (B), (C) ऐसे हैं कि \(A\subseteq B\subseteq C\), तो ((C-A)-(B-A)) किसके बराबर है?
If (A), (B), (C) satisfy \(A\subseteq B\subseteq C\), then ((C-A)-(B-A)) is equal to which set?
#sets
#subset-chain
#difference
#identity
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A (C-B)
B (B-A)
C (C-A)
D (A)
Explanation opens after your attempt
Step 1
Concept
Removing (B-A) from (C-A) leaves the elements inside (C) but outside (B). Hence the result is (C-B).
Step 2
Why this answer is correct
The correct answer is A. (C-B). Removing (B-A) from (C-A) leaves the elements inside (C) but outside (B). Hence the result is (C-B).
Step 3
Exam Tip
(C-A) में से (B-A) हटाने पर (B) के बाहर और (C) के अंदर वाले तत्व बचते हैं। इसलिए परिणाम (C-B) है।
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यदि \(A\cap B=B\cap C=C\cap A=\varnothing\), (n(A)=12), (n(B)=15), (n(C)=18), तो (n\(A\cup B\cup C\)) क्या है?
If \(A\cap B=B\cap C=C\cap A=\varnothing\), (n(A)=12), (n(B)=15), (n(C)=18), what is (n\(A\cup B\cup C\))?
#sets
#disjoint
#three-sets
#cardinality
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A (,45,)
B (,30,)
C (,33,)
D (,18,)
Explanation opens after your attempt
Step 1
Concept
The three sets are pairwise disjoint, so the union count is the direct sum. (12+15+18=45).
Step 2
Why this answer is correct
The correct answer is A. (,45,). The three sets are pairwise disjoint, so the union count is the direct sum. (12+15+18=45).
Step 3
Exam Tip
तीनों समुच्चय परस्पर असंबद्ध हैं, इसलिए संघ की संख्या सीधा योग है। (12+15+18=45)।
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\(यदि (A={x\in\mathbb{N}:x\le30,\ x\) पूर्ण वर्ग है\(}) और (B={x\in\mathbb{N}:x\le30,\ 3\mid x}), तो (A-B) क्या है\)?
\(If (A={x\in\mathbb{N}:x\le30,\ x\) is a perfect square\(}) and (B={x\in\mathbb{N}:x\le30,\ 3\mid x}), what is (A-B)\)?
#sets
#perfect-squares
#difference
#number-sets
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A ({1,4,16,25})
B ({9})
C ({1,4,9,16,25})
D ({3,6,9,12,15,18,21,24,27,30})
Explanation opens after your attempt
Correct Answer
A. ({1,4,16,25})
Step 1
Concept
Perfect squares up to (30) are ({1,4,9,16,25}). Removing (9), which is divisible by (3), gives ({1,4,16,25}).
Step 2
Why this answer is correct
The correct answer is A. ({1,4,16,25}). Perfect squares up to (30) are ({1,4,9,16,25}). Removing (9), which is divisible by (3), gives ({1,4,16,25}).
Step 3
Exam Tip
(30) तक पूर्ण वर्ग ({1,4,9,16,25}) हैं। इनमें (3) से विभाज्य (9) हटाने पर ({1,4,16,25}) मिलता है।
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यदि \(A={x\in\mathbb{Z}:x^2\le25}\), \(B={x\in\mathbb{Z}:x\ge0}\) और \(C={x\in\mathbb{Z}:x<4}\), तो \(A\cap B\cap C\) क्या है?
If \(A={x\in\mathbb{Z}:x^2\le25}\), \(B={x\in\mathbb{Z}:x\ge0}\), and \(C={x\in\mathbb{Z}:x<4}\), what is \(A\cap B\cap C\)?
#sets
#integers
#intersection
#three-sets
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A ({0,1,2,3})
B ({-5,-4,-3,-2,-1,0,1,2,3})
C ({4,5})
D ({0,1,2,3,4,5})
Explanation opens after your attempt
Correct Answer
A. ({0,1,2,3})
Step 1
Concept
(A) contains integers from (-5) to (5). Applying \(x\ge0\) and (x<4) gives ({0,1,2,3}).
Step 2
Why this answer is correct
The correct answer is A. ({0,1,2,3}). (A) contains integers from (-5) to (5). Applying \(x\ge0\) and (x<4) gives ({0,1,2,3}).
Step 3
Exam Tip
(A) में (-5) से (5) तक पूर्णांक हैं। \(x\ge0\) और (x<4) लगाने पर ({0,1,2,3}) मिलता है।
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यदि \(A={x\in\mathbb{R}:x\ne0}\) और \(B={x\in\mathbb{R}:x^2>0}\), तो \(A\triangle B\) क्या है?
If \(A={x\in\mathbb{R}:x\ne0}\) and \(B={x\in\mathbb{R}:x^2>0}\), what is \(A\triangle B\)?
#sets
#symmetric-difference
#equal-sets
#real-numbers
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A \(\varnothing\)
B ({0})
C \(\mathbb{R}\)
D \(\mathbb{R}-{0}\)
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\)
Step 1
Concept
For real numbers, \(x^2>0\) exactly when \(x\ne0\). Thus (A=B), and the symmetric difference is \(\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). For real numbers, \(x^2>0\) exactly when \(x\ne0\). Thus (A=B), and the symmetric difference is \(\varnothing\).
Step 3
Exam Tip
वास्तविक संख्याओं में \(x^2>0\) ठीक तब होता है जब \(x\ne0\)। इसलिए (A=B) और सममित अंतर \(\varnothing\) है।
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यदि (A) और (B) सीमित समुच्चय हैं तथा (n\(A\cup B\)=n(A)+n(B)), तो कौन-सा निष्कर्ष सही है?
If (A) and (B) are finite sets and (n\(A\cup B\)=n(A)+n(B)), which conclusion is correct?
#sets
#cardinality
#disjoint
#union
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A \(A\cap B=\varnothing\)
B (A=B)
C \(A\subseteq B\)
D \(B\subseteq A\)
Explanation opens after your attempt
Correct Answer
A. \(A\cap B=\varnothing\)
Step 1
Concept
In the general formula, (n\(A\cap B\)) is subtracted. The equality holds only when (n\(A\cap B\)=0), that is \(A\cap B=\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(A\cap B=\varnothing\). In the general formula, (n\(A\cap B\)) is subtracted. The equality holds only when (n\(A\cap B\)=0), that is \(A\cap B=\varnothing\).
Step 3
Exam Tip
सामान्य सूत्र में (n\(A\cap B\)) घटता है। योग बराबर तभी होगा जब (n\(A\cap B\)=0), यानी \(A\cap B=\varnothing\)।
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यदि (A-B=A) और (B-C=B) हैं, तो कौन-सा कथन अवश्य सत्य है?
If (A-B=A) and (B-C=B), which statement must be true?
#sets
#difference
#disjoint
#reasoning
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A \(A\cap B=\varnothing\) और \(B\cap C=\varnothing\)
B \(A\subseteq B\) और \(B\subseteq C\)
C (A=B=C)
D \(A\cup B=C\)
Explanation opens after your attempt
Correct Answer
A. \(A\cap B=\varnothing\) और \(B\cap C=\varnothing\)
Step 1
Concept
(A-B=A) means \(A\cap B=\varnothing\). Similarly, (B-C=B) means \(B\cap C=\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(A\cap B=\varnothing\) और \(B\cap C=\varnothing\). (A-B=A) means \(A\cap B=\varnothing\). Similarly, (B-C=B) means \(B\cap C=\varnothing\).
Step 3
Exam Tip
(A-B=A) का अर्थ \(A\cap B=\varnothing\) है। इसी तरह (B-C=B) का अर्थ \(B\cap C=\varnothing\) है।
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यदि \(A={x\in\mathbb{R}:x\ge2}\), \(B={x\in\mathbb{R}:x<6}\) और \(C={x\in\mathbb{R}:x=4}\), तो (\(A\cap B\)-C) क्या है?
If \(A={x\in\mathbb{R}:x\ge2}\), \(B={x\in\mathbb{R}:x<6}\), and \(C={x\in\mathbb{R}:x=4}\), what is (\(A\cap B\)-C)?
#sets
#intervals
#intersection
#difference
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A ([2,4)\cup(4,6))
B ([2,6))
C ((2,6))
D \([2,4]\cup[4,6\))
Explanation opens after your attempt
Correct Answer
A. ([2,4)\cup(4,6))
Step 1
Concept
\(A\cap B=[2,6\)). Removing (4) from it gives ([2,4)\cup(4,6)).
Step 2
Why this answer is correct
The correct answer is A. ([2,4)\cup(4,6)). \(A\cap B=[2,6\)). Removing (4) from it gives ([2,4)\cup(4,6)).
Step 3
Exam Tip
\(A\cap B=[2,6\)) है। इसमें से (4) हटाने पर ([2,4)\cup(4,6)) मिलता है।
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यदि (n\(A\cup B\cup C\)=88), (n(A-B)=19), (n(B-A)=24), (n\(A\cap B\)=13) और (C-\(A\cup B\)) में (32) तत्व हैं, तो (n(\(A\cup B\)-C)) क्या है यदि (C) में \(A\cup B\) का कोई तत्व नहीं है?
If (n\(A\cup B\cup C\)=88), (n(A-B)=19), (n(B-A)=24), (n\(A\cap B\)=13), and (C-\(A\cup B\)) has (32) elements, what is (n(\(A\cup B\)-C)) if (C) has no element of \(A\cup B\)?
#sets
#cardinality
#difference
#three-sets
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A (,56,)
B (,32,)
C (,45,)
D (,75,)
Explanation opens after your attempt
Step 1
Concept
Since (C) and \(A\cup B\) are disjoint, (\(A\cup B\)-C=A\cup B). Its value is (19+24+13=56).
Step 2
Why this answer is correct
The correct answer is A. (,56,). Since (C) and \(A\cup B\) are disjoint, (\(A\cup B\)-C=A\cup B). Its value is (19+24+13=56).
Step 3
Exam Tip
क्योंकि (C) और \(A\cup B\) असंबद्ध हैं, इसलिए (\(A\cup B\)-C=A\cup B)। इसका मान (19+24+13=56) है।
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