यदि \(A={x\in\mathbb{Z}: -2\le x<5}\) और \(B={x\in\mathbb{Z}: x^2\le 9}\) हैं, तो (A-B) क्या है?
If \(A={x\in\mathbb{Z}: -2\le x<5}\) and \(B={x\in\mathbb{Z}: x^2\le 9}\), then what is (A-B)?
#sets
#operations
#difference
#integers
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A (A-B={4})
B (A-B={-2,4})
C (A-B={-2,-1,0,1,2})
D \(A-B=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. (A-B={4})
Step 1
Concept
\(A=\{-2,-1,0,1,2,3,4\}\) and \(B=\{-3,-2,-1,0,1,2,3\}\), so only (4) remains. In exams, list both sets clearly before taking difference.
Step 2
Why this answer is correct
The correct answer is A. (A-B={4}). \(A=\{-2,-1,0,1,2,3,4\}\) and \(B=\{-3,-2,-1,0,1,2,3\}\), so only (4) remains. In exams, list both sets clearly before taking difference.
Step 3
Exam Tip
\(A=\{-2,-1,0,1,2,3,4\}\) और \(B=\{-3,-2,-1,0,1,2,3\}\) है, इसलिए केवल (4) बचता है। परीक्षा में अंतर निकालते समय पहले दोनों समुच्चय स्पष्ट लिखें।
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यदि (n(A)=40), (n(B)=36), (n(C)=28), (n\(A\cap B\)=14), (n\(B\cap C\)=10), (n\(C\cap A\)=12) और (n\(A\cap B\cap C\)=5) है, तो (n(\(A\cup B\cup C\)-C)) कितना है?
If (n(A)=40), (n(B)=36), (n(C)=28), (n\(A\cap B\)=14), (n\(B\cap C\)=10), (n\(C\cap A\)=12), and (n\(A\cap B\cap C\)=5), then what is (n(\(A\cup B\cup C\)-C))?
#sets
#three-sets
#cardinality
#difference
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A (45)
B (73)
C (28)
D (50)
Explanation opens after your attempt
Step 1
Concept
First (n\(A\cup B\cup C\)=73), then removing (28) elements of (C) leaves (45). In such questions, find the complete union first.
Step 2
Why this answer is correct
The correct answer is A. (45). First (n\(A\cup B\cup C\)=73), then removing (28) elements of (C) leaves (45). In such questions, find the complete union first.
Step 3
Exam Tip
पहले (n\(A\cup B\cup C\)=73) मिलता है, फिर (C) के (28) तत्व हटाने पर (45) बचते हैं। ऐसे प्रश्न में पहले पूरा संघ निकालें।
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यदि \(A\cup B={1,2,3,4,5,6}\), \(A\cap B={2,5}\) और (A-B={1,4}) है, तो (B-A) क्या होगा?
If \(A\cup B={1,2,3,4,5,6}\), \(A\cap B={2,5}\), and (A-B={1,4}), what is (B-A)?
#sets
#operations
#union
#intersection
#difference
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A (B-A={3,6})
B (B-A={1,4})
C (B-A={2,5})
D (B-A={1,2,4,5})
Explanation opens after your attempt
Correct Answer
A. (B-A={3,6})
Step 1
Concept
\(A\cup B\) is split into (A-B), \(A\cap B\), and (B-A). The remaining elements are (3) and (6).
Step 2
Why this answer is correct
The correct answer is A. (B-A={3,6}). \(A\cup B\) is split into (A-B), \(A\cap B\), and (B-A). The remaining elements are (3) and (6).
Step 3
Exam Tip
\(A\cup B\) को तीन भागों (A-B), \(A\cap B\) और (B-A) में बांटा जाता है। बचे हुए तत्व (3) और (6) हैं।
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यदि \(A={x\in\mathbb{R}: -2<x\le 6}\), \(B={x\in\mathbb{R}: 1\le x<8}\) और \(C={x\in\mathbb{R}: 4<x\le 10}\), तो (\(A\cup C\)-B) क्या है?
If \(A={x\in\mathbb{R}: -2<x\le 6}\), \(B={x\in\mathbb{R}: 1\le x<8}\), and \(C={x\in\mathbb{R}: 4<x\le 10}\), what is (\(A\cup C\)-B)?
#sets
#intervals
#union
#difference
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A \((-2,1)\cup[8,10]\)
B ((-2,1]\cup(8,10])
C ([1,8))
D ((-2,10])
Explanation opens after your attempt
Correct Answer
A. \((-2,1)\cup[8,10]\)
Step 1
Concept
\(A\cup C=(-2,10]), and removing (B=[1,8)\) gives \((-2,1)\cup[8,10]\). Watch open and closed endpoints carefully.
Step 2
Why this answer is correct
The correct answer is A. \((-2,1)\cup[8,10]\). \(A\cup C=(-2,10]), and removing (B=[1,8)\) gives \((-2,1)\cup[8,10]\). Watch open and closed endpoints carefully.
Step 3
Exam Tip
\(A\cup C=(-2,10]) है और (B=[1,8)\) हटाने पर \((-2,1)\cup[8,10]\) मिलता है। सिरों के खुले-बंद होने पर ध्यान दें।
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यदि (n(A)=45), (n(B)=38) और (n\(A\cup B\)=63) है, तो (n\(A\cap B\)) ज्ञात कीजिए।
If (n(A)=45), (n(B)=38), and (n\(A\cup B\)=63), find (n\(A\cap B\)).
#sets
#cardinality
#union
#intersection
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A (20)
B (18)
C (25)
D (83)
Explanation opens after your attempt
Step 1
Concept
Using (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)), (63=45+38-x), so (x=20). In exams, remember to subtract the double count.
Step 2
Why this answer is correct
The correct answer is A. (20). Using (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)), (63=45+38-x), so (x=20). In exams, remember to subtract the double count.
Step 3
Exam Tip
सूत्र (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)) से (63=45+38-x), इसलिए (x=20)। परीक्षा में अधिक गिनती को घटाना न भूलें।
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यदि (A), (B) और (C) समुच्चय हैं, तो \(A\cap(B-C)\) किसके बराबर है?
If (A), (B), and (C) are sets, then \(A\cap(B-C)\) is equal to which expression?
#sets
#identity
#intersection
#difference
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A (\(A\cap B\)-C)
B \((A-C)\cup B\)
C (A-\(B\cap C\))
D (\(A\cup B\)-C)
Explanation opens after your attempt
Correct Answer
A. (\(A\cap B\)-C)
Step 1
Concept
(B-C) contains elements in (B) and not in (C). Intersecting with (A) gives exactly (\(A\cap B\)-C).
Step 2
Why this answer is correct
The correct answer is A. (\(A\cap B\)-C). (B-C) contains elements in (B) and not in (C). Intersecting with (A) gives exactly (\(A\cap B\)-C).
Step 3
Exam Tip
(B-C) में वे तत्व हैं जो (B) में हैं और (C) में नहीं हैं। (A) से प्रतिच्छेद करने पर यही (\(A\cap B\)-C) बनता है।
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यदि \(A\subseteq B\) है, तो (\(A\cup B\)-\(A\cap B\)) किसके बराबर है?
If \(A\subseteq B\), then (\(A\cup B\)-\(A\cap B\)) is equal to which set?
#sets
#subset
#identity
#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
When \(A\subseteq B\), \(A\cup B=B\) and \(A\cap B=A\). Hence the result is (B-A).
Step 2
Why this answer is correct
The correct answer is A. (B-A). When \(A\subseteq B\), \(A\cup B=B\) and \(A\cap B=A\). Hence the result is (B-A).
Step 3
Exam Tip
जब \(A\subseteq B\), तब \(A\cup B=B\) और \(A\cap B=A\) होता है। इसलिए परिणाम (B-A) है।
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यदि \(U={1,2,\ldots,12}\), \(A=\{2,4,6,8,10,12\}\) और \(B=\{3,6,9,12\}\) हैं, तो (\(A\cup B\)') क्या है?
If \(U={1,2,\ldots,12}\), \(A=\{2,4,6,8,10,12\}\), and \(B=\{3,6,9,12\}\), what is (\(A\cup B\)')?
#sets
#complement
#union
#universal-set
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A ({1,5,7,11})
B ({6,12})
C ({2,3,4,6,8,9,10,12})
D ({1,3,5,7,9,11})
Explanation opens after your attempt
Correct Answer
A. ({1,5,7,11})
Step 1
Concept
\(A\cup B={2,3,4,6,8,9,10,12}\). The elements outside it in (U) are (1,5,7,11).
Step 2
Why this answer is correct
The correct answer is A. ({1,5,7,11}). \(A\cup B={2,3,4,6,8,9,10,12}\). The elements outside it in (U) are (1,5,7,11).
Step 3
Exam Tip
\(A\cup B={2,3,4,6,8,9,10,12}\) है। (U) में इसके बाहर के तत्व (1,5,7,11) हैं।
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यदि \(A=\{1,2,3,4,5\}\), \(B=\{2,4,6,8\}\) और \(C=\{1,4,7,8\}\) हैं, तो (A\cap\(B\cup C\)) क्या है?
If \(A=\{1,2,3,4,5\}\), \(B=\{2,4,6,8\}\), and \(C=\{1,4,7,8\}\), what is (A\cap\(B\cup C\))?
#sets
#union
#intersection
#three-sets
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A ({1,2,4})
B ({2,4,8})
C ({1,4,8})
D ({1,2,3,4,5})
Explanation opens after your attempt
Correct Answer
A. ({1,2,4})
Step 1
Concept
First \(B\cup C={1,2,4,6,7,8}\). Its intersection with (A) is ({1,2,4}).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,4}). First \(B\cup C={1,2,4,6,7,8}\). Its intersection with (A) is ({1,2,4}).
Step 3
Exam Tip
पहले \(B\cup C={1,2,4,6,7,8}\) मिलता है। इसके साथ (A) का प्रतिच्छेद ({1,2,4}) है।
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यदि \(A-B=\varnothing\) और \(B-A\ne\varnothing\) है, तो सही निष्कर्ष कौन-सा है?
If \(A-B=\varnothing\) and \(B-A\ne\varnothing\), which conclusion is correct?
#sets
#proper-subset
#difference
#reasoning
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A \(A\subset B\)
B \(B\subset A\)
C (A=B)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(A\subset B\)
Step 1
Concept
\(A-B=\varnothing\) means every element of (A) lies in (B). \(B-A\ne\varnothing\) means (B) has at least one extra element.
Step 2
Why this answer is correct
The correct answer is A. \(A\subset B\). \(A-B=\varnothing\) means every element of (A) lies in (B). \(B-A\ne\varnothing\) means (B) has at least one extra element.
Step 3
Exam Tip
\(A-B=\varnothing\) बताता है कि (A) का हर तत्व (B) में है। \(B-A\ne\varnothing\) बताता है कि (B) में कुछ अतिरिक्त तत्व हैं।
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यदि \(A\triangle B=(A-B)\cup(B-A)\) है और \(A=\{a,b,c,d\}\), \(B=\{b,d,e,f\}\) हैं, तो \(A\triangle B\) क्या है?
If \(A\triangle B=(A-B)\cup(B-A)\) and \(A=\{a,b,c,d\}\), \(B=\{b,d,e,f\}\), what is \(A\triangle B\)?
#sets
#symmetric-difference
#difference
#union
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A ({a,c,e,f})
B ({b,d})
C ({a,b,c,d,e,f})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({a,c,e,f})
Step 1
Concept
Common elements (b,d) are removed. Only elements that belong to exactly one set are taken.
Step 2
Why this answer is correct
The correct answer is A. ({a,c,e,f}). Common elements (b,d) are removed. Only elements that belong to exactly one set are taken.
Step 3
Exam Tip
समान तत्व (b,d) हट जाते हैं। केवल वे तत्व लिए जाते हैं जो ठीक एक समुच्चय में हों।
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यदि \(A\cap B=A\cap C\) और \(A\cup B=A\cup C\) हैं, तो कौन-सा निष्कर्ष सही है?
If \(A\cap B=A\cap C\) and \(A\cup B=A\cup C\), which conclusion is correct?
#sets
#proof
#union
#intersection
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A (B=C)
B (A=B=C)
C \(B\subseteq C\) मात्र
D \(C\subseteq B\) मात्र
Explanation opens after your attempt
Step 1
Concept
For every element, the conditions inside and outside (A) force (B) and (C) to match. Hence (B=C).
Step 2
Why this answer is correct
The correct answer is A. (B=C). For every element, the conditions inside and outside (A) force (B) and (C) to match. Hence (B=C).
Step 3
Exam Tip
हर तत्व के लिए (A) के अंदर और बाहर दोनों स्थितियां (B) और (C) को समान बनाती हैं। इसलिए (B=C) है।
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यदि \(A={x\in\mathbb{R}: 0\le x<3}\) और \(B={x\in\mathbb{R}: 1<x\le 5}\), तो \(A\cup B\) क्या है?
If \(A={x\in\mathbb{R}: 0\le x<3}\) and \(B={x\in\mathbb{R}: 1<x\le 5}\), what is \(A\cup B\)?
#sets
#intervals
#union
#real-numbers
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A ([0,5])
B ([0,5))
C ( (0,5])
D ([0,1]\cup(3,5])
Explanation opens after your attempt
Correct Answer
A. ([0,5])
Step 1
Concept
The intervals overlap, so their union covers all points from (0) to (5). Both endpoints (0) and (5) are included.
Step 2
Why this answer is correct
The correct answer is A. ([0,5]). The intervals overlap, so their union covers all points from (0) to (5). Both endpoints (0) and (5) are included.
Step 3
Exam Tip
दोनों अंतराल ओवरलैप करते हैं, इसलिए उनका संघ (0) से (5) तक पूरा है। दोनों सिरों (0) और (5) शामिल हैं।
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यदि \(A={x\in\mathbb{R}: -3\le x\le 2}\) और \(B={x\in\mathbb{R}: -1<x<4}\), तो (A-B) क्या है?
If \(A={x\in\mathbb{R}: -3\le x\le 2}\) and \(B={x\in\mathbb{R}: -1<x<4}\), what is (A-B)?
#sets
#intervals
#difference
#endpoints
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A ([-3,-1])
B ([-3,-1))
C ((-1,2])
D ([-3,2])
Explanation opens after your attempt
Correct Answer
A. ([-3,-1])
Step 1
Concept
(B) does not include (-1), so (-1) remains. Removing (B) from (A) gives ([-3,-1]).
Step 2
Why this answer is correct
The correct answer is A. ([-3,-1]). (B) does not include (-1), so (-1) remains. Removing (B) from (A) gives ([-3,-1]).
Step 3
Exam Tip
(B) में (-1) शामिल नहीं है, इसलिए (-1) बचता है। (A) से (B) हटाने पर ([-3,-1]) मिलता है।
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यदि (n(A-B)=12), (n(B-A)=9) और (n\(A\cap B\)=7), तो (n\(A\cup B\)) क्या है?
If (n(A-B)=12), (n(B-A)=9), and (n\(A\cap B\)=7), what is (n\(A\cup B\))?
#sets
#cardinality
#venn
#union
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A (28)
B (21)
C (19)
D (35)
Explanation opens after your attempt
Step 1
Concept
The union is the sum of three disjoint parts (A-B), (B-A), and \(A\cap B\). Thus (12+9+7=28).
Step 2
Why this answer is correct
The correct answer is A. (28). The union is the sum of three disjoint parts (A-B), (B-A), and \(A\cap B\). Thus (12+9+7=28).
Step 3
Exam Tip
संघ तीन अलग भागों (A-B), (B-A) और \(A\cap B\) का योग है। इसलिए (12+9+7=28)।
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एक कक्षा में (60) छात्रों में से (34) गणित, (28) भौतिकी और (12) दोनों पढ़ते हैं। केवल गणित पढ़ने वाले छात्रों की संख्या कितनी है?
In a class of (60) students, (34) study Mathematics, (28) study Physics, and (12) study both. How many students study only Mathematics?
#sets
#word-problem
#difference
#intersection
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A (22)
B (46)
C (12)
D (18)
Explanation opens after your attempt
Step 1
Concept
Only Mathematics (=n(M)-n\(M\cap P\)=34-12=22). In such questions, subtract the common part from the only part.
Step 2
Why this answer is correct
The correct answer is A. (22). Only Mathematics (=n(M)-n\(M\cap P\)=34-12=22). In such questions, subtract the common part from the only part.
Step 3
Exam Tip
केवल गणित (=n(M)-n\(M\cap P\)=34-12=22)। ऐसे प्रश्न में दोनों पढ़ने वालों को केवल वाले भाग से घटाएं।
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यदि (n(A)=52), (n(B)=47), (n\(A\cap B\)=21) और (n(U)=80), तो (n(\(A\cup B\)')) क्या है?
If (n(A)=52), (n(B)=47), (n\(A\cap B\)=21), and (n(U)=80), what is (n(\(A\cup B\)'))?
#sets
#cardinality
#complement
#union
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A (2)
B (78)
C (21)
D (1)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\)=52+47-21=78). Therefore the number outside is (80-78=2).
Step 2
Why this answer is correct
The correct answer is A. (2). (n\(A\cup B\)=52+47-21=78). Therefore the number outside is (80-78=2).
Step 3
Exam Tip
(n\(A\cup B\)=52+47-21=78)। अतः बाहर के तत्व (80-78=2) हैं।
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यदि \(A\cap B=\varnothing\), (n(A)=15) और (n(B)=19), तो (n\(A\cup B\)) क्या है?
If \(A\cap B=\varnothing\), (n(A)=15), and (n(B)=19), what is (n\(A\cup B\))?
#sets
#disjoint
#cardinality
#union
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A (34)
B (4)
C (285)
D (19)
Explanation opens after your attempt
Step 1
Concept
Disjoint sets have no common element. Hence (n\(A\cup B\)=15+19=34).
Step 2
Why this answer is correct
The correct answer is A. (34). Disjoint sets have no common element. Hence (n\(A\cup B\)=15+19=34).
Step 3
Exam Tip
असंबद्ध समुच्चयों में कोई सामान्य तत्व नहीं होता। इसलिए (n\(A\cup B\)=15+19=34)।
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यदि \(A\cup B=A\) है, तो (B) के बारे में सही कथन क्या है?
If \(A\cup B=A\), which statement about (B) is correct?
#sets
#subset
#union
#reasoning
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A \(B\subseteq A\)
B \(A\subseteq B\)
C \(A\cap B=\varnothing\)
D (B=A')
Explanation opens after your attempt
Correct Answer
A. \(B\subseteq A\)
Step 1
Concept
Adding (B) to (A) by union does not change (A), so every element of (B) is in (A). Thus \(B\subseteq A\).
Step 2
Why this answer is correct
The correct answer is A. \(B\subseteq A\). Adding (B) to (A) by union does not change (A), so every element of (B) is in (A). Thus \(B\subseteq A\).
Step 3
Exam Tip
संघ में (B) जोड़ने पर (A) नहीं बदलता, इसलिए (B) का हर तत्व (A) में है। अतः \(B\subseteq A\)।
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यदि \(A\cap B=B\) है, तो कौन-सा निष्कर्ष सही है?
If \(A\cap B=B\), which conclusion is correct?
#sets
#subset
#intersection
#reasoning
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A \(B\subseteq A\)
B \(A\subseteq B\)
C \(A-B=\varnothing\)
D \(A\cup B=B\)
Explanation opens after your attempt
Correct Answer
A. \(B\subseteq A\)
Step 1
Concept
The intersection equals (B) only when every element of (B) lies in (A). Hence \(B\subseteq A\).
Step 2
Why this answer is correct
The correct answer is A. \(B\subseteq A\). The intersection equals (B) only when every element of (B) lies in (A). Hence \(B\subseteq A\).
Step 3
Exam Tip
प्रतिच्छेद (B) के बराबर तभी होगा जब (B) का हर तत्व (A) में हो। इसलिए \(B\subseteq A\) है।
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यदि \(A=\{1,3,5,7,9\}\), \(B=\{2,3,5,8,9\}\) और \(C=\{3,4,5,9\}\), तो \(A\cap B\cap C\) क्या है?
If \(A=\{1,3,5,7,9\}\), \(B=\{2,3,5,8,9\}\), and \(C=\{3,4,5,9\}\), what is \(A\cap B\cap C\)?
#sets
#three-sets
#intersection
#common-elements
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A ({3,5,9})
B ({1,2,4,7,8})
C ({3,5})
D ({9})
Explanation opens after your attempt
Correct Answer
A. ({3,5,9})
Step 1
Concept
The common elements in all three sets are (3,5,9). In a three-set intersection, each element must be in all three sets.
Step 2
Why this answer is correct
The correct answer is A. ({3,5,9}). The common elements in all three sets are (3,5,9). In a three-set intersection, each element must be in all three sets.
Step 3
Exam Tip
तीनों समुच्चयों में सामान्य तत्व (3,5,9) हैं। तीन समुच्चयों के प्रतिच्छेद में हर तत्व तीनों में होना चाहिए।
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\(यदि (A={x\in\mathbb{N}: x\le 20,\ x\) is prime\(}) और (B={x\in\mathbb{N}: x<20,\ x\) is odd}), तो (A-B) क्या है?
\(If (A={x\in\mathbb{N}: x\le 20,\ x\) is prime\(}) and (B={x\in\mathbb{N}: x<20,\ x\) is odd}), what is (A-B)?
#sets
#number-sets
#difference
#prime
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A ({2})
B ({2,19})
C ({3,5,7,11,13,17,19})
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
All odd primes in (A) are in (B), so only (2) remains. (19) is also in (B) because it is odd and less than (20).
Step 2
Why this answer is correct
The correct answer is A. ({2}). All odd primes in (A) are in (B), so only (2) remains. (19) is also in (B) because it is odd and less than (20).
Step 3
Exam Tip
(A) के सभी विषम अभाज्य (B) में चले जाते हैं, केवल (2) बचता है। (19) भी (B) में है क्योंकि वह विषम और (20) से छोटा है।
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यदि \(A={x:x=2k,\ k\in\mathbb{Z}}\) और \(B={x:x=4k,\ k\in\mathbb{Z}}\), तो सही संबंध कौन-सा है?
If \(A={x:x=2k,\ k\in\mathbb{Z}}\) and \(B={x:x=4k,\ k\in\mathbb{Z}}\), which relation is correct?
#sets
#set-builder
#subset
#number-sets
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A \(B\subseteq A\)
B \(A\subseteq B\)
C \(A\cap B=\varnothing\)
D \(A-B=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(B\subseteq A\)
Step 1
Concept
Every multiple of (4) is also a multiple of (2). Therefore \(B\subseteq A\).
Step 2
Why this answer is correct
The correct answer is A. \(B\subseteq A\). Every multiple of (4) is also a multiple of (2). Therefore \(B\subseteq A\).
Step 3
Exam Tip
हर (4) का गुणज (2) का भी गुणज होता है। इसलिए \(B\subseteq A\) है।
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यदि \(A={x:x\) अंग्रेजी शब्द (MATHEMATICS) का अक्षर है(}) और \(B={x:x\) अंग्रेजी शब्द (STATISTICS) का अक्षर है(}), तो \(A\cap B\) क्या है?
If \(A={x:x\) is a letter of the English word (MATHEMATICS)(}) and \(B={x:x\) is a letter of the English word (STATISTICS)(}), what is \(A\cap B\)?
#sets
#letters
#intersection
#roster-form
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A ({A,I,M,S,T})
B ({A,C,E,H,I,M,S,T})
C ({A,C,I,S,T})
D ({M,H,E})
Explanation opens after your attempt
Correct Answer
A. ({A,I,M,S,T})
Step 1
Concept
The distinct letters common to both words are (A,I,M,S,T). Repeated letters are not counted in a set.
Step 2
Why this answer is correct
The correct answer is A. ({A,I,M,S,T}). The distinct letters common to both words are (A,I,M,S,T). Repeated letters are not counted in a set.
Step 3
Exam Tip
दोनों शब्दों में आने वाले अलग-अलग अक्षर (A,I,M,S,T) हैं। समुच्चय में दोहराए गए अक्षर नहीं गिने जाते।
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यदि \(A\cap(B-C)=\varnothing\) है, तो इसका अर्थ क्या है?
If \(A\cap(B-C)=\varnothing\), what does it mean?
#sets
#meaning
#intersection
#difference
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A (A) का कोई भी तत्व ऐसा नहीं है जो (B) में हो और (C) में न हो / No element of (A) is in (B) but not in (C)
B \(A\subseteq B-C\)
C \(B-C\subseteq A\)
D \(A\cup B=C\)
Explanation opens after your attempt
Correct Answer
A. (A) का कोई भी तत्व ऐसा नहीं है जो (B) में हो और (C) में न हो / No element of (A) is in (B) but not in (C)
Step 1
Concept
(B-C) contains elements in (B) but not in (C). Empty intersection with (A) means none of these lies in (A).
Step 2
Why this answer is correct
The correct answer is A. (A) का कोई भी तत्व ऐसा नहीं है जो (B) में हो और (C) में न हो / No element of (A) is in (B) but not in (C). (B-C) contains elements in (B) but not in (C). Empty intersection with (A) means none of these lies in (A).
Step 3
Exam Tip
(B-C) वे तत्व हैं जो (B) में हैं पर (C) में नहीं। (A) के साथ प्रतिच्छेद खाली होने का यही अर्थ है।
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यदि \(A=\{1,2,3,4\}\), तो \(A\cup\varnothing\), \(A\cap\varnothing\), और \(A-\varnothing\) क्रमशः क्या हैं?
If \(A=\{1,2,3,4\}\), what are \(A\cup\varnothing\), \(A\cap\varnothing\), and \(A-\varnothing\) respectively?
#sets
#empty-set
#operations
#identity
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A \(A,\varnothing,A\)
B \(\varnothing,A,A\)
C \(A,A,\varnothing\)
D \(\varnothing,\varnothing,A\)
Explanation opens after your attempt
Correct Answer
A. \(A,\varnothing,A\)
Step 1
Concept
The empty set adds nothing in union, gives nothing in intersection, and removes nothing in difference. Hence the answer is \(A,\varnothing,A\).
Step 2
Why this answer is correct
The correct answer is A. \(A,\varnothing,A\). The empty set adds nothing in union, gives nothing in intersection, and removes nothing in difference. Hence the answer is \(A,\varnothing,A\).
Step 3
Exam Tip
खाली समुच्चय संघ में कुछ नहीं जोड़ता, प्रतिच्छेद में कुछ सामान्य नहीं देता और अंतर में कुछ नहीं हटाता। इसलिए उत्तर \(A,\varnothing,A\) है।
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यदि \(A\cup B=U\) और \(A\cap B=\varnothing\), तो (B) किसके बराबर है?
If \(A\cup B=U\) and \(A\cap B=\varnothing\), then (B) is equal to which set?
#sets
#complement
#disjoint
#union
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A (A')
B (A)
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
(B) contains exactly the elements not in (A), and together they form (U). Thus (B=A').
Step 2
Why this answer is correct
The correct answer is A. (A'). (B) contains exactly the elements not in (A), and together they form (U). Thus (B=A').
Step 3
Exam Tip
(B) में ठीक वे तत्व हैं जो (A) में नहीं हैं और दोनों मिलकर (U) बनाते हैं। अतः (B=A')।
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यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6,8\}\) और \(C=\{1,2,8,9\}\), तो \((A-B)\cup(A-C)\) क्या है?
If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6,8\}\), and \(C=\{1,2,8,9\}\), what is \((A-B)\cup(A-C)\)?
#sets
#difference
#union
#three-sets
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A ({1,3,4,5,6})
B ({3,5})
C ({2,8})
D ({1,2,3,4,5,6})
Explanation opens after your attempt
Correct Answer
A. ({1,3,4,5,6})
Step 1
Concept
(A-B={1,3,5}) and (A-C={3,4,5,6}). Their union is ({1,3,4,5,6}).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,4,5,6}). (A-B={1,3,5}) and (A-C={3,4,5,6}). Their union is ({1,3,4,5,6}).
Step 3
Exam Tip
(A-B={1,3,5}) और (A-C={3,4,5,6}) है। इनका संघ ({1,3,4,5,6}) है।
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यदि \(A=\{2,3,5,7,11,13\}\) और \(B={x\in A:x>5}\), तो \(A\cap B\) क्या है?
If \(A=\{2,3,5,7,11,13\}\) and \(B={x\in A:x>5}\), what is \(A\cap B\)?
#sets
#set-builder
#intersection
#subset
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A ({7,11,13})
B ({2,3,5})
C ({5,7,11,13})
D (A)
Explanation opens after your attempt
Correct Answer
A. ({7,11,13})
Step 1
Concept
(B) is a subset of (A) containing elements greater than (5). Therefore \(A\cap B=B={7,11,13}\).
Step 2
Why this answer is correct
The correct answer is A. ({7,11,13}). (B) is a subset of (A) containing elements greater than (5). Therefore \(A\cap B=B={7,11,13}\).
Step 3
Exam Tip
(B), (A) का उपसमुच्चय है जिसमें (5) से बड़े तत्व हैं। इसलिए \(A\cap B=B={7,11,13}\)।
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यदि \(A={x\in\mathbb{Z}: |x|\le 3}\) और \(B={x\in\mathbb{Z}: x^2-2x\le 0}\), तो \(A\cap B\) क्या है?
If \(A={x\in\mathbb{Z}: |x|\le 3}\) and \(B={x\in\mathbb{Z}: x^2-2x\le 0}\), what is \(A\cap B\)?
#sets
#inequality
#intersection
#integers
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A ({0,1,2})
B ({-3,-2,-1,0,1,2,3})
C ({1,2})
D ({0,2,3})
Explanation opens after your attempt
Correct Answer
A. ({0,1,2})
Step 1
Concept
\(x^2-2x\le0\) gives \(0\le x\le2\). In integers, \(B=\{0,1,2\}\), which is also in (A).
Step 2
Why this answer is correct
The correct answer is A. ({0,1,2}). \(x^2-2x\le0\) gives \(0\le x\le2\). In integers, \(B=\{0,1,2\}\), which is also in (A).
Step 3
Exam Tip
\(x^2-2x\le0\) से \(0\le x\le2\) मिलता है। पूर्णांकों में \(B=\{0,1,2\}\), जो (A) में भी है।
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यदि \(A={x\in\mathbb{N}: x\mid 36}\) और \(B={x\in\mathbb{N}: x\mid 48}\), तो \(A\cap B\) क्या है?
If \(A={x\in\mathbb{N}: x\mid 36}\) and \(B={x\in\mathbb{N}: x\mid 48}\), what is \(A\cap B\)?
#sets
#divisors
#intersection
#number-theory
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A ({1,2,3,4,6,12})
B ({1,2,3,4,6,8,9,12,16,18,24,36,48})
C ({12})
D ({1,2,4,8,16,48})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4,6,12})
Step 1
Concept
Common divisors of (36) and (48) are divisors of (\gcd(36,48)=12). Hence the set is ({1,2,3,4,6,12}).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4,6,12}). Common divisors of (36) and (48) are divisors of (\gcd(36,48)=12). Hence the set is ({1,2,3,4,6,12}).
Step 3
Exam Tip
सामान्य भाजक (36) और (48) के (\gcd(36,48)=12) के भाजक होते हैं। इसलिए ({1,2,3,4,6,12}) मिलेगा।
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यदि \(A={x\in\mathbb{N}: x\mid 18}\) और \(B={x\in\mathbb{N}: x\mid 24}\), तो \(A\cup B\) क्या है?
If \(A={x\in\mathbb{N}: x\mid 18}\) and \(B={x\in\mathbb{N}: x\mid 24}\), what is \(A\cup B\)?
#sets
#divisors
#union
#number-theory
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A ({1,2,3,4,6,8,9,12,18,24})
B ({1,2,3,6})
C ({1,2,3,6,18,24})
D ({4,8,9,12})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4,6,8,9,12,18,24})
Step 1
Concept
Divisors of (18) are ({1,2,3,6,9,18}), and divisors of (24) are ({1,2,3,4,6,8,12,24}). Combining without repetition gives the union.
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4,6,8,9,12,18,24}). Divisors of (18) are ({1,2,3,6,9,18}), and divisors of (24) are ({1,2,3,4,6,8,12,24}). Combining without repetition gives the union.
Step 3
Exam Tip
(18) के भाजक ({1,2,3,6,9,18}) और (24) के भाजक ({1,2,3,4,6,8,12,24}) हैं। दोनों को बिना दोहराव मिलाने पर सही संघ मिलता है।
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यदि \(A={x\in\mathbb{R}: x^2<9}\) और \(B={x\in\mathbb{R}: x\ge 1}\), तो (A-B) क्या है?
If \(A={x\in\mathbb{R}: x^2<9}\) and \(B={x\in\mathbb{R}: x\ge 1}\), what is (A-B)?
#sets
#quadratic-inequality
#difference
#intervals
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A ((-3,1))
B ((-3,1])
C ([-3,1))
D ((1,3))
Explanation opens after your attempt
Correct Answer
A. ((-3,1))
Step 1
Concept
(A=(-3,3)), and (B) contains (1) and all greater real numbers. Therefore (A-B=(-3,1)).
Step 2
Why this answer is correct
The correct answer is A. ((-3,1)). (A=(-3,3)), and (B) contains (1) and all greater real numbers. Therefore (A-B=(-3,1)).
Step 3
Exam Tip
(A=(-3,3)) है और (B) में (1) तथा उससे बड़े सभी वास्तविक संख्याएं हैं। इसलिए (A-B=(-3,1)) है।
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यदि \(A={x\in\mathbb{R}: x<0}\), \(B={x\in\mathbb{R}: x^2\le4}\), तो \(A\cup B\) क्या है?
If \(A={x\in\mathbb{R}: x<0}\), \(B={x\in\mathbb{R}: x^2\le4}\), what is \(A\cup B\)?
#sets
#real-numbers
#union
#intervals
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A (\(-\infty,2]\)
B ([-2,2])
C (\(-\infty,0\))
D ([0,2])
Explanation opens after your attempt
Correct Answer
A. (\(-\infty,2]\)
Step 1
Concept
(B=[-2,2]), and (A) gives all negative numbers. Together they form (\(-\infty,2]\).
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,2]\). (B=[-2,2]), and (A) gives all negative numbers. Together they form (\(-\infty,2]\).
Step 3
Exam Tip
(B=[-2,2]) और (A) सभी ऋणात्मक संख्याएं देता है। मिलाकर (\(-\infty,2]\) मिलता है।
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यदि \(A={x\in\mathbb{Z}: -5\le x\le5}\) और \(B={x\in\mathbb{Z}: x\) विषम है(}), तो \(A\cap B\) क्या है?
If \(A={x\in\mathbb{Z}: -5\le x\le5}\) and \(B={x\in\mathbb{Z}: x\) is odd(}), what is \(A\cap B\)?
#sets
#integers
#intersection
#odd-numbers
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A ({-5,-3,-1,1,3,5})
B ({-4,-2,0,2,4})
C ({-5,-4,-3,-2,-1,0,1,2,3,4,5})
D ({1,3,5})
Explanation opens after your attempt
Correct Answer
A. ({-5,-3,-1,1,3,5})
Step 1
Concept
(A) contains integers from (-5) to (5). The odd elements among them are ({-5,-3,-1,1,3,5}).
Step 2
Why this answer is correct
The correct answer is A. ({-5,-3,-1,1,3,5}). (A) contains integers from (-5) to (5). The odd elements among them are ({-5,-3,-1,1,3,5}).
Step 3
Exam Tip
(A) में (-5) से (5) तक के पूर्णांक हैं। इनमें विषम तत्व ({-5,-3,-1,1,3,5}) हैं।
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यदि (A-B=A) है, तो कौन-सा कथन सही है?
If (A-B=A), which statement is correct?
#sets
#difference
#disjoint
#reasoning
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A \(A\cap B=\varnothing\)
B \(A\subseteq B\)
C \(B\subseteq A\)
D (A=B)
Explanation opens after your attempt
Correct Answer
A. \(A\cap B=\varnothing\)
Step 1
Concept
Removing (B) does not change (A), so (A) and (B) have no common element. Thus \(A\cap B=\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(A\cap B=\varnothing\). Removing (B) does not change (A), so (A) and (B) have no common element. Thus \(A\cap B=\varnothing\).
Step 3
Exam Tip
(B) हटाने पर (A) में कोई बदलाव नहीं हुआ, इसलिए (A) और (B) में कोई सामान्य तत्व नहीं है। अतः \(A\cap B=\varnothing\)।
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यदि (A-B=B-A) है, तो सही निष्कर्ष कौन-सा है?
If (A-B=B-A), which conclusion is correct?
#sets
#difference
#equality
#reasoning
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A (A=B)
B \(A\cap B=\varnothing\)
C \(A\subset B\)
D \(B\subset A\)
Explanation opens after your attempt
Step 1
Concept
If an element lies only in (A), it is in (A-B) but not in (B-A). For equality, no such element can exist, so (A=B).
Step 2
Why this answer is correct
The correct answer is A. (A=B). If an element lies only in (A), it is in (A-B) but not in (B-A). For equality, no such element can exist, so (A=B).
Step 3
Exam Tip
यदि कोई तत्व केवल (A) में हो तो वह (A-B) में होगा पर (B-A) में नहीं। समानता के लिए ऐसे तत्व नहीं हो सकते, इसलिए (A=B)।
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यदि \(A\cup B=A\cap B\) है, तो क्या निष्कर्ष निकलेगा?
If \(A\cup B=A\cap B\), what conclusion follows?
#sets
#union
#intersection
#equality
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A (A=B)
B \(A\cap B=\varnothing\)
C \(A=\varnothing\) और \(B\ne\varnothing\)
D \(A\ne B\)
Explanation opens after your attempt
Step 1
Concept
Always \(A\cap B\subseteq A\cup B\). They can be equal only when (A) and (B) are the same set.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Always \(A\cap B\subseteq A\cup B\). They can be equal only when (A) and (B) are the same set.
Step 3
Exam Tip
सदैव \(A\cap B\subseteq A\cup B\) होता है। दोनों बराबर तभी हो सकते हैं जब (A) और (B) समान हों।
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यदि \(A=\{1,2,3\}\) और \(B=\{3,4\}\), तो (\mathcal{P}\(A\cap B\)) में कितने तत्व हैं?
If \(A=\{1,2,3\}\) and \(B=\{3,4\}\), how many elements are in (\mathcal{P}\(A\cap B\))?
#sets
#power-set
#intersection
#cardinality
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A (2)
B (1)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(A\cap B={3}\), which has (1) element. Hence its power set has \(2^1=2\) elements.
Step 2
Why this answer is correct
The correct answer is A. (2). \(A\cap B={3}\), which has (1) element. Hence its power set has \(2^1=2\) elements.
Step 3
Exam Tip
\(A\cap B={3}\) है, जिसमें (1) तत्व है। इसलिए इसके घात समुच्चय में \(2^1=2\) तत्व होंगे।
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यदि \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6\}\), तो (\mathcal{P}(A-B)) में कितने उपसमुच्चय हैं?
If \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), how many subsets are in (\mathcal{P}(A-B))?
#sets
#power-set
#difference
#cardinality
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A (4)
B (2)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
(A-B={1,2}), which has (2) elements. Its power set has \(2^2=4\) subsets.
Step 2
Why this answer is correct
The correct answer is A. (4). (A-B={1,2}), which has (2) elements. Its power set has \(2^2=4\) subsets.
Step 3
Exam Tip
(A-B={1,2}) है, जिसमें (2) तत्व हैं। घात समुच्चय में \(2^2=4\) उपसमुच्चय होंगे।
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यदि (n\(A\cup B\)=75), (n(A-B)=28) और (n(B-A)=31), तो (n\(A\cap B\)) क्या है?
If (n\(A\cup B\)=75), (n(A-B)=28), and (n(B-A)=31), what is (n\(A\cap B\))?
#sets
#cardinality
#venn
#intersection
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A (16)
B (59)
C (44)
D (12)
Explanation opens after your attempt
Step 1
Concept
The union is made of disjoint parts (A-B), (B-A), and \(A\cap B\). So (75=28+31+x), hence (x=16).
Step 2
Why this answer is correct
The correct answer is A. (16). The union is made of disjoint parts (A-B), (B-A), and \(A\cap B\). So (75=28+31+x), hence (x=16).
Step 3
Exam Tip
संघ (A-B), (B-A) और \(A\cap B\) के असंबद्ध भागों से बनता है। इसलिए (75=28+31+x), अतः (x=16)।
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यदि \(A=\{1,2,3,4,5,6,7,8\}\), \(B=\{2,4,6,8,10\}\), तो (\(A\cup B\)-\(A\cap B\)) क्या है?
If \(A=\{1,2,3,4,5,6,7,8\}\), \(B=\{2,4,6,8,10\}\), what is (\(A\cup B\)-\(A\cap B\))?
#sets
#symmetric-difference
#union
#intersection
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A ({1,3,5,7,10})
B ({2,4,6,8})
C ({1,2,3,4,5,6,7,8,10})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,7,10})
Step 1
Concept
This is the symmetric difference, where common elements are removed. Removing common elements (2,4,6,8) gives ({1,3,5,7,10}).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,7,10}). This is the symmetric difference, where common elements are removed. Removing common elements (2,4,6,8) gives ({1,3,5,7,10}).
Step 3
Exam Tip
यह सममित अंतर है, जिसमें सामान्य तत्व हट जाते हैं। सामान्य तत्व (2,4,6,8) हटाने पर ({1,3,5,7,10}) मिलता है।
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यदि \(A\cap B=\varnothing\), तो (A-(A-B)) किसके बराबर है?
If \(A\cap B=\varnothing\), then (A-(A-B)) is equal to which set?
#sets
#disjoint
#difference
#identity
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A \(\varnothing\)
B (A)
C (B)
D \(A\cup B\)
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\)
Step 1
Concept
When \(A\cap B=\varnothing\), (A-B=A). Hence (A-(A-B)=A-A=\varnothing).
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). When \(A\cap B=\varnothing\), (A-B=A). Hence (A-(A-B)=A-A=\varnothing).
Step 3
Exam Tip
जब \(A\cap B=\varnothing\), तब (A-B=A) होता है। इसलिए (A-(A-B)=A-A=\varnothing)।
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कौन-सा विकल्प (A\cap\(B\cup C\)) के बराबर है?
Which option is equal to (A\cap\(B\cup C\))?
#sets
#distributive-law
#intersection
#union
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A (\(A\cap B\)\cup\(A\cap C\))
B (\(A\cup B\)\cap\(A\cup C\))
C \((A-B)\cup C\)
D (A\cup\(B\cap C\))
Explanation opens after your attempt
Correct Answer
A. (\(A\cap B\)\cup\(A\cap C\))
Step 1
Concept
Intersection distributes over union. Hence (A\cap\(B\cup C\)=\(A\cap B\)\cup\(A\cap C\)).
Step 2
Why this answer is correct
The correct answer is A. (\(A\cap B\)\cup\(A\cap C\)). Intersection distributes over union. Hence (A\cap\(B\cup C\)=\(A\cap B\)\cup\(A\cap C\)).
Step 3
Exam Tip
प्रतिच्छेद संघ पर वितरित होता है। इसलिए (A\cap\(B\cup C\)=\(A\cap B\)\cup\(A\cap C\))।
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कौन-सा विकल्प (A\cup\(B\cap C\)) के बराबर है?
Which option is equal to (A\cup\(B\cap C\))?
#sets
#distributive-law
#union
#intersection
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A (\(A\cup B\)\cap\(A\cup C\))
B (\(A\cap B\)\cup\(A\cap C\))
C (A-\(B\cap C\))
D (\(A\cup B\)-C)
Explanation opens after your attempt
Correct Answer
A. (\(A\cup B\)\cap\(A\cup C\))
Step 1
Concept
Union distributes over intersection. Hence (A\cup\(B\cap C\)=\(A\cup B\)\cap\(A\cup C\)).
Step 2
Why this answer is correct
The correct answer is A. (\(A\cup B\)\cap\(A\cup C\)). Union distributes over intersection. Hence (A\cup\(B\cap C\)=\(A\cup B\)\cap\(A\cup C\)).
Step 3
Exam Tip
संघ प्रतिच्छेद पर वितरित होता है। इसलिए (A\cup\(B\cap C\)=\(A\cup B\)\cap\(A\cup C\))।
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यदि \(A={x\in\mathbb{N}: x\le 15}\), \(B={x\in\mathbb{N}: 3\mid x}\) और \(C={x\in\mathbb{N}: 5\mid x}\), तो (A\cap\(B\cup C\)) क्या है?
If \(A={x\in\mathbb{N}: x\le 15}\), \(B={x\in\mathbb{N}: 3\mid x}\), and \(C={x\in\mathbb{N}: 5\mid x}\), what is (A\cap\(B\cup C\))?
#sets
#number-sets
#union
#intersection
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A ({3,5,6,9,10,12,15})
B ({15})
C ({3,6,9,12})
D ({5,10,15})
Explanation opens after your attempt
Correct Answer
A. ({3,5,6,9,10,12,15})
Step 1
Concept
Numbers up to (15) divisible by (3) or (5) are taken. They are ({3,5,6,9,10,12,15}).
Step 2
Why this answer is correct
The correct answer is A. ({3,5,6,9,10,12,15}). Numbers up to (15) divisible by (3) or (5) are taken. They are ({3,5,6,9,10,12,15}).
Step 3
Exam Tip
(15) तक (3) या (5) से विभाज्य संख्याएं ली जाती हैं। वे ({3,5,6,9,10,12,15}) हैं।
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यदि \(A={x\in\mathbb{N}: x\le 30,\ 2\mid x}\) और \(B={x\in\mathbb{N}: x\le 30,\ 3\mid x}\), तो \(A\cap B\) क्या है?
If \(A={x\in\mathbb{N}: x\le 30,\ 2\mid x}\) and \(B={x\in\mathbb{N}: x\le 30,\ 3\mid x}\), what is \(A\cap B\)?
#sets
#multiples
#intersection
#number-sets
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A ({6,12,18,24,30})
B \({2,4,6,\ldots,30}\)
C \({3,6,9,\ldots,30}\)
D ({1,6,12,18,24,30})
Explanation opens after your attempt
Correct Answer
A. ({6,12,18,24,30})
Step 1
Concept
Numbers divisible by both (2) and (3) are divisible by (6). Up to (30), these are ({6,12,18,24,30}).
Step 2
Why this answer is correct
The correct answer is A. ({6,12,18,24,30}). Numbers divisible by both (2) and (3) are divisible by (6). Up to (30), these are ({6,12,18,24,30}).
Step 3
Exam Tip
जो संख्याएं (2) और (3) दोनों से विभाज्य हैं, वे (6) से विभाज्य हैं। (30) तक ऐसी संख्याएं ({6,12,18,24,30}) हैं।
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यदि \(A=\{1,2,3,4,5\}\), \(B=\{2,3,6\}\) और \(C=\{3,4,7\}\), तो (A-\(B\cap C\)) क्या है?
If \(A=\{1,2,3,4,5\}\), \(B=\{2,3,6\}\), and \(C=\{3,4,7\}\), what is (A-\(B\cap C\))?
#sets
#difference
#intersection
#three-sets
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A ({1,2,4,5})
B ({3})
C ({1,5})
D ({1,2,3,4,5})
Explanation opens after your attempt
Correct Answer
A. ({1,2,4,5})
Step 1
Concept
\(B\cap C={3}\). Removing (3) from (A) gives ({1,2,4,5}).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,4,5}). \(B\cap C={3}\). Removing (3) from (A) gives ({1,2,4,5}).
Step 3
Exam Tip
\(B\cap C={3}\) है। (A) से (3) हटाने पर ({1,2,4,5}) मिलता है।
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यदि \(A={x\in\mathbb{Z}: -4\le x\le4}\) और \(B={x\in\mathbb{Z}: x^2\ge9}\), तो \(A\cap B\) क्या है?
If \(A={x\in\mathbb{Z}: -4\le x\le4}\) and \(B={x\in\mathbb{Z}: x^2\ge9}\), what is \(A\cap B\)?
#sets
#inequality
#intersection
#integers
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A ({-4,-3,3,4})
B ({-3,3})
C ({-4,-3,-2,2,3,4})
D ({-2,-1,0,1,2})
Explanation opens after your attempt
Correct Answer
A. ({-4,-3,3,4})
Step 1
Concept
(A) contains integers from (-4) to (4). Among them, \(x^2\ge9\) is true only for (-4,-3,3,4).
Step 2
Why this answer is correct
The correct answer is A. ({-4,-3,3,4}). (A) contains integers from (-4) to (4). Among them, \(x^2\ge9\) is true only for (-4,-3,3,4).
Step 3
Exam Tip
(A) में (-4) से (4) तक पूर्णांक हैं। इनमें \(x^2\ge9\) केवल (-4,-3,3,4) के लिए सत्य है।
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यदि (A), (B) और (C) ऐसे समुच्चय हैं कि (A-B=A-C) और \(A\cap B=A\cap C\), तो (A) के संदर्भ में कौन-सा कथन सही है?
If (A), (B), and (C) are sets such that (A-B=A-C) and \(A\cap B=A\cap C\), which statement is correct with respect to (A)?
#sets
#advanced-reasoning
#difference
#intersection
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A (A) के अंदर (B) और (C) समान व्यवहार करते हैं / (B) and (C) behave the same inside (A)
B (B=C) अवश्य / (B=C) necessarily
C \(A=\varnothing\) अवश्य / \(A=\varnothing\) necessarily
D \(B\cap C=\varnothing\) अवश्य / \(B\cap C=\varnothing\) necessarily
Explanation opens after your attempt
Correct Answer
A. (A) के अंदर (B) और (C) समान व्यवहार करते हैं / (B) and (C) behave the same inside (A)
Step 1
Concept
The two given parts make membership of (B) and (C) the same inside (A). Outside (A), (B) and (C) may differ.
Step 2
Why this answer is correct
The correct answer is A. (A) के अंदर (B) और (C) समान व्यवहार करते हैं / (B) and (C) behave the same inside (A). The two given parts make membership of (B) and (C) the same inside (A). Outside (A), (B) and (C) may differ.
Step 3
Exam Tip
दिए गए दोनों भाग (A) के भीतर (B) और (C) की सदस्यता को समान बनाते हैं। (A) के बाहर (B) और (C) अलग हो सकते हैं।
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