यदि \(A=\{2,4,6,8,10\}\), \(B=\{1,2,3,4,5\}\) और \(C=\{4,5,6,7\}\) है, तो (A\cap\(B\cup C\)) क्या है?
If \(A=\{2,4,6,8,10\}\), \(B=\{1,2,3,4,5\}\), and \(C=\{4,5,6,7\}\), what is (A\cap\(B\cup C\))?
#sets
#mixed-operations
#union-intersection
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A ( {2,4,6} )
B ( {4,6} )
C ( {1,2,3,4,5,6,7} )
D ( {8,10} )
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Correct Answer
A. ( {2,4,6} )
Explanation
Simple Explanation
पहले \(B\cup C={1,2,3,4,5,6,7}\) है। इसका (A) से प्रतिच्छेद ({2,4,6}) है। / First \(B\cup C={1,2,3,4,5,6,7}\). Its intersection with (A) is ({2,4,6}).
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\(यदि (A={x:x\in \mathbb{N}, 1\le x\le 30, x\) का गुणज 2 है\(}) और (B={x:x\in \mathbb{N}, 1\le x\le 30, x\) का गुणज 3 है\(}), तो (A\cap B) में कितने अवयव हैं\)?
\(If (A={x:x\in \mathbb{N}, 1\le x\le 30, x\) is a multiple of \(2}) and (B={x:x\in \mathbb{N}, 1\le x\le 30, x\) is a multiple of \(3}), how many elements are in (A\cap B)\)?
#sets
#multiples
#intersection
#cardinality
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A (5)
B (10)
C (15)
D (6)
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Explanation
Simple Explanation
\(A\cap B\) में (2) और (3) दोनों के गुणज, यानी (6) के गुणज आएंगे। (30) तक ऐसे अवयव ({6,12,18,24,30}) हैं। / \(A\cap B\) contains multiples of both (2) and (3), that is, multiples of (6). Up to (30), these elements are ({6,12,18,24,30}).
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यदि \(P=\{a,b,c,d\}\) और \(Q=\{b,d,e\}\) है, तो \(P\cap Q\) ज्ञात कीजिए।
If \(P=\{a,b,c,d\}\) and \(Q=\{b,d,e\}\), find \(P\cap Q\).
#sets
#intersection
#common-elements
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A ( {a,c,e} )
B ( {b,d} )
C ( {a,b,c,d,e} )
D \( \varnothing \)
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Correct Answer
B. ( {b,d} )
Explanation
Simple Explanation
\(P\cap Q\) में केवल वे अवयव आते हैं जो दोनों में समान हों। समान अवयव ढूंढना सबसे पहला कदम रखें। / \(P\cap Q\) contains only elements common to both sets. Finding common elements should be the first step.
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\(यदि (A={x:x\in \mathbb{N}, x\le 15}) और (B={x:x\in \mathbb{N}, x\) विषम है\(, x\le 15}) है, तो (A-B) क्या है\)?
\(If (A={x:x\in \mathbb{N}, x\le 15}) and (B={x:x\in \mathbb{N}, x\) is odd\(, x\le 15}), what is (A-B)\)?
#sets
#natural-numbers
#difference
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A ( {1,3,5,7,9,11,13,15} )
B ( {2,4,6,8,10,12,14} )
C ( {2,4,6,8,10,12,14,16} )
D \( \varnothing \)
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Correct Answer
B. ( {2,4,6,8,10,12,14} )
Explanation
Simple Explanation
(A-B) में (A) के वे अवयव रहेंगे जो (B) में नहीं हैं। इसलिए (15) तक की सम संख्याएं उत्तर हैं। / (A-B) keeps elements of (A) that are not in (B). So the even numbers up to (15) are the answer.
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,5,7\}\) और \(B=\{2,4,5,8,10\}\) है, तो (\(A\cap B\)') क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,5,7\}\), and \(B=\{2,4,5,8,10\}\), what is (\(A\cap B\)')?
#sets
#complement
#intersection
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A ( {2,5} )
B ( {1,3,4,6,7,8,9,10} )
C ( {1,2,4,5,7,8,10} )
D ( {3,6,9} )
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Correct Answer
B. ( {1,3,4,6,7,8,9,10} )
Explanation
Simple Explanation
पहले \(A\cap B={2,5}\) है। (U) में इसके बाहर के अवयव ({1,3,4,6,7,8,9,10}) हैं। / First \(A\cap B={2,5}\). The elements outside it in (U) are ({1,3,4,6,7,8,9,10}).
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यदि (n(A)=35), (n(B)=27) और (n\(A\cup B\)=50), तो (n(A-B)) क्या है?
If (n(A)=35), (n(B)=27), and (n\(A\cup B\)=50), what is (n(A-B))?
#sets
#cardinality
#difference
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A (8)
B (12)
C (23)
D (15)
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Explanation
Simple Explanation
पहले (n\(A\cap B\)=35+27-50=12) है। इसलिए (n(A-B)=35-12=23)। / First (n\(A\cap B\)=35+27-50=12). Therefore (n(A-B)=35-12=23).
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एक समूह में (24) विद्यार्थी हिंदी, (18) विद्यार्थी अंग्रेजी और (7) विद्यार्थी दोनों पढ़ते हैं। केवल हिंदी पढ़ने वाले विद्यार्थियों की संख्या क्या है?
In a group, (24) students study Hindi, (18) students study English, and (7) students study both. How many students study only Hindi?
#sets
#word-problem
#difference
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A (17)
B (35)
C (31)
D (11)
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Explanation
Simple Explanation
केवल हिंदी का अर्थ (H-E) है। संख्या (24-7=17) होगी। / Only Hindi means (H-E). The number is (24-7=17).
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यदि \(A=\{2,4,6,8,10\}\) और \(B=\{1,2,3,4\}\) है, तो (B-A) क्या है?
If \(A=\{2,4,6,8,10\}\) and \(B=\{1,2,3,4\}\), what is (B-A)?
#sets
#difference
#order
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A ( {1,3} )
B ( {6,8,10} )
C ( {2,4} )
D ( {1,2,3,4,6,8,10} )
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Correct Answer
A. ( {1,3} )
Explanation
Simple Explanation
(B-A) में (B) से (A) के सामान्य अवयव हटा दिए जाते हैं। इसलिए (1) और (3) बचते हैं। / In (B-A), common elements with (A) are removed from (B). So (1) and (3) remain.
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यदि (A=[-1,4]) और (B=(1,6)), तो \(A\cap B\) क्या है?
If (A=[-1,4]) and (B=(1,6)), what is \(A\cap B\)?
#sets
#intervals
#intersection
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A ( [-1,6) )
B ( (1,4] )
C ( [1,4] )
D ( (-1,1] )
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Correct Answer
B. ( (1,4] )
Explanation
Simple Explanation
दोनों अंतरालों का सामान्य भाग (1) से (4) तक है। (1) शामिल नहीं और (4) शामिल है, इसलिए ((1,4]) सही है। / The common part of both intervals is from (1) to (4). Since (1) is not included and (4) is included, ((1,4]) is correct.
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यदि \(A={x:x^2-7x+12=0}\) और \(B={x:x^2-9x+20=0}\), तो \(A\cup B\) क्या है?
If \(A={x:x^2-7x+12=0}\) and \(B={x:x^2-9x+20=0}\), what is \(A\cup B\)?
#sets
#quadratic
#union
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A ( {3,4,5} )
B ( {3,4} )
C ( {4,5} )
D ( {3,5} )
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Correct Answer
A. ( {3,4,5} )
Explanation
Simple Explanation
\(A=\{3,4\}\) और \(B=\{4,5\}\) है। संघ में दोहराया अवयव (4) केवल एक बार लिखा जाता है। / \(A=\{3,4\}\) and \(B=\{4,5\}\). In a union, the repeated element (4) is written only once.
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यदि \(A=\{1,2,3,4\}\), \(B=\{3,4,5\}\) और \(C=\{4,5,6\}\) है, तो (\(A\cup B\)\cap C) क्या है?
If \(A=\{1,2,3,4\}\), \(B=\{3,4,5\}\), and \(C=\{4,5,6\}\), what is (\(A\cup B\)\cap C)?
#sets
#mixed-operations
#intersection
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A ( {4,5} )
B ( {3,4} )
C ( {1,2,3,4,5,6} )
D ( {5,6} )
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Correct Answer
A. ( {4,5} )
Explanation
Simple Explanation
पहले \(A\cup B={1,2,3,4,5}\) है। इसका (C) से सामान्य भाग ({4,5}) है। / First \(A\cup B={1,2,3,4,5}\). Its common part with (C) is ({4,5}).
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यदि \(A=\{1,4,9,16,25\}\) और \(B=\{2,4,8,16,32\}\), तो \((A-B)\cup(B-A)\) क्या है?
If \(A=\{1,4,9,16,25\}\) and \(B=\{2,4,8,16,32\}\), what is \((A-B)\cup(B-A)\)?
#sets
#symmetric-difference
#application
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A ( {4,16} )
B ( {1,2,8,9,25,32} )
C ( {1,4,9,16,25,2,8,32} )
D \( \varnothing \)
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Correct Answer
B. ( {1,2,8,9,25,32} )
Explanation
Simple Explanation
(A-B={1,9,25}) और (B-A={2,8,32}) है। दोनों का संघ ({1,2,8,9,25,32}) है। / (A-B={1,9,25}) and (B-A={2,8,32}). Their union is ({1,2,8,9,25,32}).
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यदि \(A=\{1,3,5,7,9\}\), \(B=\{2,3,5,8\}\) और \(C=\{3,4,5,6\}\) है, तो (A-\(B\cap C\)) क्या है?
If \(A=\{1,3,5,7,9\}\), \(B=\{2,3,5,8\}\), and \(C=\{3,4,5,6\}\), what is (A-\(B\cap C\))?
#sets
#difference
#compound
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A ( {1,7,9} )
B ( {3,5} )
C ( {1,3,5,7,9} )
D ( {2,4,6,8} )
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Correct Answer
A. ( {1,7,9} )
Explanation
Simple Explanation
\(B\cap C={3,5}\) है। इन्हें (A) से हटाने पर ({1,7,9}) मिलता है। / \(B\cap C={3,5}\). Removing these from (A) gives ({1,7,9}).
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यदि (n(A)=18), (n(B)=14) और (n\(A\cap B\)=6), तो (n\(A\cup B\)) क्या है?
If (n(A)=18), (n(B)=14), and (n\(A\cap B\)=6), what is (n\(A\cup B\))?
#sets
#cardinality
#union-formula
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A (26)
B (32)
C (38)
D (20)
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Explanation
Simple Explanation
सूत्र (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)) लगाइए। इसलिए (18+14-6=26)। / Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). Thus (18+14-6=26).
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यदि (n\(A\cup B\)=45), (n(A)=28) और (n(B)=25), तो (n\(A\cap B\)) ज्ञात कीजिए।
If (n\(A\cup B\)=45), (n(A)=28), and (n(B)=25), find (n\(A\cap B\)).
#sets
#cardinality
#intersection
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A (8)
B (12)
C (17)
D (53)
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Explanation
Simple Explanation
(n\(A\cap B\)=n(A)+n(B)-n\(A\cup B\)) है। इसलिए (28+25-45=8)। / (n\(A\cap B\)=n(A)+n(B)-n\(A\cup B\)). Therefore (28+25-45=8).
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एक कक्षा में (30) विद्यार्थी गणित, (22) विद्यार्थी भौतिकी और (12) विद्यार्थी दोनों पढ़ते हैं। कम से कम एक विषय पढ़ने वाले विद्यार्थियों की संख्या क्या है?
In a class, (30) students study Mathematics, (22) students study Physics, and (12) students study both. How many students study at least one subject?
#sets
#word-problem
#union
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A (40)
B (52)
C (64)
D (20)
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Explanation
Simple Explanation
कम से कम एक का अर्थ \(M\cup P\) है। संख्या (30+22-12=40) होगी। / At least one means \(M\cup P\). The number is (30+22-12=40).
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\(यदि (A={x:x\in \mathbb{Z}, -2\le x\le 4}) और (B={x:x\in \mathbb{Z}, x\) विषम है\(}) है, तो (A\cap B) क्या है\)?
\(If (A={x:x\in \mathbb{Z}, -2\le x\le 4}) and (B={x:x\in \mathbb{Z}, x\) is odd\(}), what is (A\cap B)\)?
#sets
#set-builder
#integers
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A ( {-1,1,3} )
B ( {-2,0,2,4} )
C ( {-2,-1,0,1,2,3,4} )
D ( {1,3,5} )
Explanation opens after your attempt
Correct Answer
A. ( {-1,1,3} )
Explanation
Simple Explanation
(A) में (-2) से (4) तक के पूर्णांक हैं। इनमें विषम पूर्णांक (-1,1,3) हैं। / (A) contains integers from (-2) to (4). The odd integers among them are (-1,1,3).
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यदि (A=[1,5]) और (B=[3,8]), तो \(A\cap B\) कौन-सा अंतराल है?
If (A=[1,5]) and (B=[3,8]), which interval is \(A\cap B\)?
#sets
#intervals
#intersection
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A ( [1,8] )
B ( [3,5] )
C ( [1,3] )
D ( [5,8] )
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Correct Answer
B. ( [3,5] )
Explanation
Simple Explanation
दोनों अंतरालों में सामान्य भाग (3) से (5) तक है। बंद सिरों को ध्यान से रखें। / The common part of both intervals is from (3) to (5). Keep closed endpoints carefully.
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यदि (A=(2,7)) और (B=[5,9]), तो \(A\cup B\) क्या होगा?
If (A=(2,7)) and (B=[5,9]), what is \(A\cup B\)?
#sets
#intervals
#union
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A ( (2,9] )
B ( [2,9] )
C ( [5,7) )
D ( (2,5) )
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Correct Answer
A. ( (2,9] )
Explanation
Simple Explanation
दोनों अंतराल (5) से (7) के बीच जुड़ते हैं। (2) शामिल नहीं और (9) शामिल है, इसलिए ((2,9]) सही है। / The intervals overlap between (5) and (7). Since (2) is not included and (9) is included, ((2,9]) is correct.
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यदि (A=[0,6]) और (B=(2,4)), तो (A-B) क्या है?
If (A=[0,6]) and (B=(2,4)), what is (A-B)?
#sets
#intervals
#difference
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A \( [0,2]\cup[4,6] \)
B ( [0,2)\cup(4,6] )
C ( (2,4) )
D ( [2,4] )
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Correct Answer
A. \( [0,2]\cup[4,6] \)
Explanation
Simple Explanation
(B=(2,4)) में (2) और (4) शामिल नहीं हैं। इसलिए (A-B) में (2) और (4) रहेंगे। / (B=(2,4)) does not include (2) and (4). So (2) and (4) remain in (A-B).
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यदि \(A={x:x^2=9}\) और \(B={x:x^2-4=0}\), तो \(A\cup B\) क्या है?
If \(A={x:x^2=9}\) and \(B={x:x^2-4=0}\), what is \(A\cup B\)?
#sets
#equations
#union
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A ( {-3,3,-2,2} )
B ( {-3,3} )
C ( {-2,2} )
D \( \varnothing \)
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Correct Answer
A. ( {-3,3,-2,2} )
Explanation
Simple Explanation
\(A=\{-3,3\}\) और \(B=\{-2,2\}\) है। संघ में दोनों के सभी अवयव आते हैं। / \(A=\{-3,3\}\) and \(B=\{-2,2\}\). The union contains all elements from both sets.
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यदि \(A={x:x^2-5x+6=0}\) और \(B={x:x^2-3x+2=0}\), तो \(A\cap B\) क्या होगा?
If \(A={x:x^2-5x+6=0}\) and \(B={x:x^2-3x+2=0}\), what is \(A\cap B\)?
#sets
#quadratic
#intersection
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A ( {1,2,3} )
B ( {2} )
C ( {3} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
B. ( {2} )
Explanation
Simple Explanation
पहले \(A=\{2,3\}\) और \(B=\{1,2\}\) निकालें। दोनों में समान अवयव केवल (2) है। / First get \(A=\{2,3\}\) and \(B=\{1,2\}\). The only common element is (2).
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किस विकल्प में (A-\(A\cap B\)) के बराबर समुच्चय दिया है?
Which option gives a set equal to (A-\(A\cap B\))?
#sets
#identity
#difference
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A (A-B)
B \(A\cup B\)
C (B-A)
D \(A\cap B\)
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Explanation
Simple Explanation
\(A\cap B\) को (A) से हटाने पर (A) का केवल (B) से बाहर वाला भाग बचता है। यही (A-B) है। / Removing \(A\cap B\) from (A) leaves the part of (A) outside (B). This is (A-B).
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कौन-सा नियम (A\cap\(B\cup C\)) के बराबर है?
Which law gives an expression equal to (A\cap\(B\cup C\))?
#sets
#distributive-law
#identity
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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\(A\cap C\) )
Explanation
Simple Explanation
यह प्रतिच्छेद का संघ पर वितरण नियम है। सूत्र याद रखने से मिश्रित क्रियाओं में गलती कम होती है। / This is the distributive law of intersection over union. Remembering the formula reduces mistakes in mixed operations.
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कौन-सा व्यंजक (\(A\cup B\)-A) के बराबर है?
Which expression is equal to (\(A\cup B\)-A)?
#sets
#set-difference
#identity
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A (A-B)
B (B-A)
C \(A\cap B\)
D \(A\cup B\)
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Explanation
Simple Explanation
\(A\cup B\) से (A) हटाने पर (B) का वह भाग बचता है जो (A) में नहीं है। इसलिए उत्तर (B-A) है। / Removing (A) from \(A\cup B\) leaves the part of (B) not in (A). Therefore the answer is (B-A).
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यदि \(A=\{1,2,3\}\) और \(B=\{4,5\}\), तो \(A\cap B\) क्या है?
If \(A=\{1,2,3\}\) and \(B=\{4,5\}\), what is \(A\cap B\)?
#sets
#disjoint
#intersection
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A ( {1,2,3,4,5} )
B ( {1,4} )
C \( \varnothing \)
D ( {3,4} )
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Correct Answer
C. \( \varnothing \)
Explanation
Simple Explanation
दोनों समुच्चयों में कोई समान अवयव नहीं है। ऐसे समुच्चय असंयुक्त होते हैं और प्रतिच्छेद \(\varnothing\) होता है। / There is no common element in the two sets. Such sets are disjoint and their intersection is \(\varnothing\).
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यदि \(A\cap B=\varnothing\), (n(A)=9) और (n(B)=11), तो (n\(A\cup B\)) क्या होगा?
If \(A\cap B=\varnothing\), (n(A)=9), and (n(B)=11), what is (n\(A\cup B\))?
#sets
#disjoint
#cardinality
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A (2)
B (20)
C (99)
D (11)
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Explanation
Simple Explanation
असंयुक्त समुच्चयों में (n\(A\cap B\)=0) होता है। इसलिए (n\(A\cup B\)=9+11=20)। / For disjoint sets, (n\(A\cap B\)=0). Hence (n\(A\cup B\)=9+11=20).
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{2,4,6,8\}\) और \(B=\{1,2,3,4\}\), तो \(A'\cap B\) क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{2,4,6,8\}\), and \(B=\{1,2,3,4\}\), what is \(A'\cap B\)?
#sets
#complement
#intersection
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A ( {1,3} )
B ( {2,4} )
C ( {5,7,9} )
D ( {1,2,3,4} )
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Correct Answer
A. ( {1,3} )
Explanation
Simple Explanation
(A'={1,3,5,7,9}) है। इसका (B) से सामान्य भाग ({1,3}) है। / (A'={1,3,5,7,9}). Its common part with (B) is ({1,3}).
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यदि \(A=\{1,2,3,4,5\}\) और \(B=\{2,4,6\}\), तो (\(A\cup B\)-\(A\cap B\)) क्या है?
If \(A=\{1,2,3,4,5\}\) and \(B=\{2,4,6\}\), what is (\(A\cup B\)-\(A\cap B\))?
#sets
#symmetric-difference
#compound
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A ( {2,4} )
B ( {1,3,5,6} )
C ( {1,2,3,4,5,6} )
D \( \varnothing \)
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Correct Answer
B. ( {1,3,5,6} )
Explanation
Simple Explanation
\(A\cup B={1,2,3,4,5,6}\) और \(A\cap B={2,4}\) है। अंतर लेने पर ({1,3,5,6}) मिलता है। / \(A\cup B={1,2,3,4,5,6}\) and \(A\cap B={2,4}\). Taking the difference gives ({1,3,5,6}).
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यदि (A-B={1,5}), (B-A={7}) और \(A\cap B={2,3}\), तो \(A\cup B\) क्या होगा?
If (A-B={1,5}), (B-A={7}), and \(A\cap B={2,3}\), what is \(A\cup B\)?
#sets
#venn-parts
#union
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A ( {1,2,3,5,7} )
B ( {1,5,7} )
C ( {2,3} )
D ( {1,2,5} )
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Correct Answer
A. ( {1,2,3,5,7} )
Explanation
Simple Explanation
संघ में (A-B), (B-A) और \(A\cap B\) के सभी भाग आते हैं। इन्हें मिलाने पर ({1,2,3,5,7}) मिलता है। / The union contains all parts (A-B), (B-A), and \(A\cap B\). Combining them gives ({1,2,3,5,7}).
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यदि (n(A-B)=13) और (n\(A\cap B\)=7), तो (n(A)) क्या है?
If (n(A-B)=13) and (n\(A\cap B\)=7), what is (n(A))?
#sets
#cardinality
#difference
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A (6)
B (20)
C (91)
D (13)
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Explanation
Simple Explanation
(A) दो अलग भागों (A-B) और \(A\cap B\) से बनता है। इसलिए (n(A)=13+7=20)। / (A) is made of two disjoint parts (A-B) and \(A\cap B\). Hence (n(A)=13+7=20).
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\(यदि (A={x:x\) अंग्रेजी वर्णमाला का स्वर है\(}) और (B={a,b,c,d,e}), तो (A\cap B) क्या है\)?
\(If (A={x:x\) is a vowel in the English alphabet\(}) and (B={a,b,c,d,e}), what is (A\cap B)\)?
#sets
#application
#intersection
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A ( {a,e} )
B ( {b,c,d} )
C ( {a,b,c,d,e} )
D ( {i,o,u} )
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Correct Answer
A. ( {a,e} )
Explanation
Simple Explanation
अंग्रेजी स्वरों में (a,e,i,o,u) होते हैं। (B) में इनमें से (a) और (e) मौजूद हैं। / English vowels are (a,e,i,o,u). Among these, (a) and (e) are present in (B).
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\(यदि (A={x:x\) अभाज्य संख्या है\(, x<15}) और (B={x:x\) विषम संख्या है\(, x<15}), तो (A-B) क्या है\)?
\(If (A={x:x\) is a prime number\(, x<15}) and (B={x:x\) is an odd number\(, x<15}), what is (A-B)\)?
#sets
#prime-numbers
#difference
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A ( {2} )
B ( {3,5,7,11,13} )
C ( {2,3,5,7,11,13} )
D \( \varnothing \)
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Correct Answer
A. ( {2} )
Explanation
Simple Explanation
\(A=\{2,3,5,7,11,13\}\) है और (B) में विषम संख्याएं हैं। (A) में केवल (2) विषम नहीं है। / \(A=\{2,3,5,7,11,13\}\), and (B) contains odd numbers. Only (2) in (A) is not odd.
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यदि \(A=\{2,3,5,7\}\) और \(B=\{5,7,11,13\}\), तो \(A\cup B\) में कितने अवयव हैं?
If \(A=\{2,3,5,7\}\) and \(B=\{5,7,11,13\}\), how many elements are in \(A\cup B\)?
#sets
#union
#counting
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A (4)
B (6)
C (8)
D (2)
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Explanation
Simple Explanation
\(A\cup B={2,3,5,7,11,13}\) है। इसलिए इसमें (6) अवयव हैं। / \(A\cup B={2,3,5,7,11,13}\). Therefore it has (6) elements.
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यदि \(A=\{1,2,3,4,5,6\}\) और \(B=\{2,4,6\}\), तो कौन-सा कथन सही है?
If \(A=\{1,2,3,4,5,6\}\) and \(B=\{2,4,6\}\), which statement is correct?
#sets
#reasoning
#subset
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A (A-B={1,3,5})
B (B-A={2,4,6})
C \(A\cap B={1,3,5}\)
D \(A\cup B=B\)
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Correct Answer
A. (A-B={1,3,5})
Explanation
Simple Explanation
\(B\subseteq A\) है, इसलिए (A-B) में (A) के वे अवयव हैं जो (B) में नहीं हैं। वे ({1,3,5}) हैं। / Since \(B\subseteq A\), (A-B) contains elements of (A) not in (B). They are ({1,3,5}).
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यदि \(A\cup B=A\), तो सही निष्कर्ष क्या है?
If \(A\cup B=A\), what is the correct conclusion?
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#subset
#reasoning
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A \(B\subseteq A\)
B \(A\subseteq B\)
C \(A\cap B=\varnothing\)
D \(A-B=\varnothing\)
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Correct Answer
A. \(B\subseteq A\)
Explanation
Simple Explanation
यदि \(A\cup B=A\), तो (B) का कोई नया अवयव (A) के बाहर नहीं है। इसलिए \(B\subseteq A\)। / If \(A\cup B=A\), (B) adds no new element outside (A). Therefore \(B\subseteq A\).
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किसी सर्वसमुच्चय (U) के लिए \(A\cup A'\) किसके बराबर है?
For a universal set (U), \(A\cup A'\) is equal to which set?
#sets
#complement
#law
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A (A)
B (A')
C (U)
D \( \varnothing \)
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Explanation
Simple Explanation
कोई भी अवयव या तो (A) में होगा या (A') में। इसलिए दोनों का संघ (U) होता है। / Every element is either in (A) or in (A'). Hence their union is (U).
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किसी सर्वसमुच्चय (U) के लिए \(A\cap A'\) किसके बराबर है?
For a universal set (U), \(A\cap A'\) is equal to which set?
#sets
#complement
#intersection
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A (U)
B (A)
C (A')
D \( \varnothing \)
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Correct Answer
D. \( \varnothing \)
Explanation
Simple Explanation
कोई अवयव एक साथ (A) और (A') दोनों में नहीं हो सकता। इसलिए प्रतिच्छेद \(\varnothing\) है। / No element can be in both (A) and (A') at the same time. Therefore the intersection is \(\varnothing\).
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यदि \(A=\{1,2,3,4,5\}\), \(B=\{2,3,6\}\) और \(C=\{3,4,7\}\), तो (A\cap\(B\cup C\)) क्या है?
If \(A=\{1,2,3,4,5\}\), \(B=\{2,3,6\}\), and \(C=\{3,4,7\}\), what is (A\cap\(B\cup C\))?
#sets
#distributive
#calculation
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A ( {2,3,4} )
B ( {1,5} )
C ( {3} )
D ( {2,3,4,6,7} )
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Correct Answer
A. ( {2,3,4} )
Explanation
Simple Explanation
\(B\cup C={2,3,4,6,7}\) है। इसका (A) से सामान्य भाग ({2,3,4}) है। / \(B\cup C={2,3,4,6,7}\). Its common part with (A) is ({2,3,4}).
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यदि \(A=\{1,2,4,8\}\), \(B=\{2,4,6\}\) और \(C=\{4,6,8\}\), तो (\(A\cap B\)\cup C) क्या है?
If \(A=\{1,2,4,8\}\), \(B=\{2,4,6\}\), and \(C=\{4,6,8\}\), what is (\(A\cap B\)\cup C)?
#sets
#mixed-operations
#union
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A ( {2,4,6,8} )
B ( {4} )
C ( {1,2,4,6,8} )
D ( {2,6} )
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Correct Answer
A. ( {2,4,6,8} )
Explanation
Simple Explanation
\(A\cap B={2,4}\) है। इसे \(C=\{4,6,8\}\) से मिलाने पर ({2,4,6,8}) मिलता है। / \(A\cap B={2,4}\). Combining it with \(C=\{4,6,8\}\) gives ({2,4,6,8}).
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\(यदि (A={x:x\) का गुणज 3 है\(, 1\le x\le 20}) और (B={x:x\) का गुणज 5 है\(, 1\le x\le 20}), तो (A\cap B) क्या है\)?
\(If (A={x:x\) is a multiple of \(3, 1\le x\le 20}) and (B={x:x\) is a multiple of \(5, 1\le x\le 20}), what is (A\cap B)\)?
#sets
#multiples
#intersection
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A ( {15} )
B ( {3,5,15} )
C ( {6,10,15} )
D \( \varnothing \)
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Correct Answer
A. ( {15} )
Explanation
Simple Explanation
(3) और (5) दोनों के गुणज में (15) ही (20) तक आता है। इसलिए प्रतिच्छेद ({15}) है। / Only (15) up to (20) is a multiple of both (3) and (5). Hence the intersection is ({15}).
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\(यदि (A={x:x\) का गुणज 4 है\(, 1\le x\le 25}) और (B={x:x\) का गुणज 6 है\(, 1\le x\le 25}), तो (A\cup B) में कितने अवयव हैं\)?
\(If (A={x:x\) is a multiple of \(4, 1\le x\le 25}) and (B={x:x\) is a multiple of \(6, 1\le x\le 25}), how many elements are in (A\cup B)\)?
#sets
#multiples
#cardinality
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A (8)
B (9)
C (10)
D (11)
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Explanation
Simple Explanation
\(A=\{4,8,12,16,20,24\}\) और \(B=\{6,12,18,24\}\) है। संघ में (9) अलग अवयव हैं। / \(A=\{4,8,12,16,20,24\}\) and \(B=\{6,12,18,24\}\). The union has (9) distinct elements.
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यदि \(A=\{1,2,3,4,5,6,7\}\) और \(B=\{2,4,6,8\}\), तो (A-B) और (B-A) का संघ क्या है?
If \(A=\{1,2,3,4,5,6,7\}\) and \(B=\{2,4,6,8\}\), what is the union of (A-B) and (B-A)?
#sets
#symmetric-difference
#difference
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A ( {1,3,5,7,8} )
B ( {2,4,6} )
C ( {1,2,3,4,5,6,7,8} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {1,3,5,7,8} )
Explanation
Simple Explanation
(A-B={1,3,5,7}) और (B-A={8}) है। उनका संघ ({1,3,5,7,8}) है। / (A-B={1,3,5,7}) and (B-A={8}). Their union is ({1,3,5,7,8}).
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\(यदि (A={x:x\in \mathbb{N}, x\le 12}) और (B={x:x\in \mathbb{N}, x\) वर्ग संख्या है\(, x\le 12}), तो (A-B) में कितने अवयव हैं\)?
\(If (A={x:x\in \mathbb{N}, x\le 12}) and (B={x:x\in \mathbb{N}, x\) is a square number\(, x\le 12}), how many elements are in (A-B)\)?
#sets
#natural-numbers
#difference
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A (3)
B (9)
C (12)
D (10)
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Explanation
Simple Explanation
(A) में (12) अवयव हैं और \(B=\{1,4,9\}\) है। इसलिए (A-B) में (12-3=9) अवयव होंगे। / (A) has (12) elements and \(B=\{1,4,9\}\). Thus (A-B) has (12-3=9) elements.
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कौन-सा विकल्प हमेशा सत्य है?
Which option is always true?
#sets
#true-statement
#reasoning
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A \(A\cup B=A\cap B\)
B (A-B=B-A)
C \(A\cap B\subseteq A\)
D \(A\subseteq A-B\)
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Correct Answer
C. \(A\cap B\subseteq A\)
Explanation
Simple Explanation
\(A\cap B\) में केवल (A) और (B) के सामान्य अवयव होते हैं, इसलिए यह (A) का उपसमुच्चय है। हमेशा सत्य कथनों को उदाहरण से भी जांचें। / \(A\cap B\) contains only common elements of (A) and (B), so it is a subset of (A). Test always-true statements with examples too.
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कौन-सा विकल्प सामान्यतः सत्य नहीं है?
Which option is generally not true?
#sets
#common-mistake
#difference
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A \(A\cup B=B\cup A\)
B \(A\cap B=B\cap A\)
C (A-B=B-A)
D \(A\cup \varnothing=A\)
Explanation opens after your attempt
Correct Answer
C. (A-B=B-A)
Explanation
Simple Explanation
समुच्चय अंतर में क्रम महत्वपूर्ण है, इसलिए (A-B) और (B-A) सामान्यतः समान नहीं होते। संघ और प्रतिच्छेद क्रमविनिमेय होते हैं। / Order matters in set difference, so (A-B) and (B-A) are generally not equal. Union and intersection are commutative.
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यदि \(A=\{1,2,3\}\), तो \(A\cup \varnothing\) क्या है?
If \(A=\{1,2,3\}\), what is \(A\cup \varnothing\)?
#sets
#empty-set
#union
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A \( \varnothing \)
B ( {1,2,3} )
C ( {0,1,2,3} )
D ( {1} )
Explanation opens after your attempt
Correct Answer
B. ( {1,2,3} )
Explanation
Simple Explanation
रिक्त समुच्चय में कोई अवयव नहीं होता, इसलिए संघ में कुछ नया नहीं जुड़ता। अतः \(A\cup \varnothing=A\)। / The empty set has no element, so it adds nothing to the union. Hence \(A\cup \varnothing=A\).
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यदि \(A=\{1,2,3\}\), तो \(A\cap \varnothing\) क्या है?
If \(A=\{1,2,3\}\), what is \(A\cap \varnothing\)?
#sets
#empty-set
#intersection
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A (A)
B ( {1,2,3} )
C \( \varnothing \)
D ( {0} )
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Correct Answer
C. \( \varnothing \)
Explanation
Simple Explanation
रिक्त समुच्चय में कोई अवयव नहीं है, इसलिए कोई सामान्य अवयव नहीं मिलेगा। अतः प्रतिच्छेद \(\varnothing\) है। / The empty set has no element, so there is no common element. Thus the intersection is \(\varnothing\).
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यदि \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6\}\), तो (n(A-B)+n(B-A)) क्या है?
If \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), what is (n(A-B)+n(B-A))?
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#cardinality
#difference
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A (2)
B (4)
C (6)
D (8)
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Explanation
Simple Explanation
(A-B={1,2}) और (B-A={5,6}) है। इसलिए (n(A-B)+n(B-A)=2+2=4)। / (A-B={1,2}) and (B-A={5,6}). Hence (n(A-B)+n(B-A)=2+2=4).
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यदि (n\(A\cup B\)=60), (n(A-B)=18) और (n(B-A)=22), तो (n\(A\cap B\)) क्या है?
If (n\(A\cup B\)=60), (n(A-B)=18), and (n(B-A)=22), what is (n\(A\cap B\))?
#sets
#venn-diagram
#cardinality
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A (20)
B (40)
C (18)
D (22)
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Explanation
Simple Explanation
\(A\cup B\) तीन अलग भागों (A-B), (B-A) और \(A\cap B\) से बनता है। इसलिए (n\(A\cap B\)=60-18-22=20)। / \(A\cup B\) is made of three disjoint parts (A-B), (B-A), and \(A\cap B\). Thus (n\(A\cap B\)=60-18-22=20).
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