यदि (n(A)=42), (n(B)=35) और (n\(A\cup B\)=60) है, तो (n\(A\cap B\)) कितना होगा?
If (n(A)=42), (n(B)=35), and (n\(A\cup B\)=60), then what is (n\(A\cap B\))?
#sets
#union
#intersection
#cardinality
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A (17)
B (15)
C (18)
D (20)
Explanation opens after your attempt
Step 1
Concept
Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). In exams, do not forget to subtract the common part.
Step 2
Why this answer is correct
The correct answer is A. (17). Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). In exams, do not forget to subtract the common part.
Step 3
Exam Tip
सूत्र (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)) लगाइए। परीक्षा में संघ के प्रश्न में समान भाग घटाना न भूलें।
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यदि (n\(A\setminus B\)=28) और (n\(A\cap B\)=16) है, तो (n(A)) कितना है?
If (n\(A\setminus B\)=28) and (n\(A\cap B\)=16), then what is (n(A))?
#sets
#difference
#intersection
#cardinality
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A (44)
B (12)
C (28)
D (16)
Explanation opens after your attempt
Step 1
Concept
The set (A) splits into disjoint parts \(A\setminus B\) and \(A\cap B\). Hence (n(A)=28+16=44).
Step 2
Why this answer is correct
The correct answer is A. (44). The set (A) splits into disjoint parts \(A\setminus B\) and \(A\cap B\). Hence (n(A)=28+16=44).
Step 3
Exam Tip
समुच्चय (A) दो असंबद्ध भागों \(A\setminus B\) और \(A\cap B\) में बंटता है। इसलिए (n(A)=28+16=44)।
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यदि \(A={x:x\in\mathbb{Z},-3\le x\le 5}\) और \(B={x:x\in\mathbb{Z},x^2\le 9}\) है, तो \(A\setminus B\) क्या है?
If \(A={x:x\in\mathbb{Z},-3\le x\le 5}\) and \(B={x:x\in\mathbb{Z},x^2\le 9}\), then what is \(A\setminus B\)?
#sets
#set-builder
#difference
#integers
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A ({4,5})
B ({-3,-2,-1,0,1,2,3})
C ({-3,4,5})
D ({1,2,3,4,5})
Explanation opens after your attempt
Correct Answer
A. ({4,5})
Step 1
Concept
Here \(B=\{-3,-2,-1,0,1,2,3\}\). Removing elements of (B) from (A) leaves ({4,5}).
Step 2
Why this answer is correct
The correct answer is A. ({4,5}). Here \(B=\{-3,-2,-1,0,1,2,3\}\). Removing elements of (B) from (A) leaves ({4,5}).
Step 3
Exam Tip
यहां \(B=\{-3,-2,-1,0,1,2,3\}\) है। (A) से (B) के तत्व हटाने पर ({4,5}) बचता है।
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यदि (A=[-2,4]) और (B=(1,6)) है, तो \(A\cap B\) क्या है?
If (A=[-2,4]) and (B=(1,6)), then what is \(A\cap B\)?
#sets
#intervals
#intersection
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A ((1,4])
B ([1,4])
C ((-2,6))
D ([-2,1])
Explanation opens after your attempt
Correct Answer
A. ((1,4])
Step 1
Concept
The common part is greater than (1) and up to (4). Therefore the correct interval is ((1,4]).
Step 2
Why this answer is correct
The correct answer is A. ((1,4]). The common part is greater than (1) and up to (4). Therefore the correct interval is ((1,4]).
Step 3
Exam Tip
साझा भाग (1) से बड़ा और (4) तक है। इसलिए सही अंतराल ((1,4]) है।
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यदि (A=\(-\infty,3]\) और \(B=[1,\infty\)) है, तो \(A\cup B\) क्या होगा?
If (A=\(-\infty,3]\) and \(B=[1,\infty\)), then what is \(A\cup B\)?
#sets
#intervals
#union
#real-numbers
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A \(\mathbb{R}\)
B ([1,3])
C (\(-\infty,1\)\cup\(3,\infty\))
D (\(-\infty,\infty\)\setminus{1,3})
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}\)
Step 1
Concept
The first interval gives all numbers up to (3), and the second gives all numbers from (1) onward. Together they form all of \(\mathbb{R}\).
Step 2
Why this answer is correct
The correct answer is A. \(\mathbb{R}\). The first interval gives all numbers up to (3), and the second gives all numbers from (1) onward. Together they form all of \(\mathbb{R}\).
Step 3
Exam Tip
पहला अंतराल (3) तक और दूसरा (1) से आगे सभी संख्याएं देता है। दोनों मिलकर पूरी \(\mathbb{R}\) बनाते हैं।
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यदि \(A=\{2,4,6,8,10,12\}\), \(B=\{3,6,9,12,15\}\) और \(C=\{6,12,18\}\) है, तो (\(A\cap B\)\setminus C) क्या है?
If \(A=\{2,4,6,8,10,12\}\), \(B=\{3,6,9,12,15\}\), and \(C=\{6,12,18\}\), then what is (\(A\cap B\)\setminus C)?
#sets
#intersection
#difference
#empty-set
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A \(\varnothing\)
B ({6,12})
C ({18})
D ({2,4,8,10})
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\)
Step 1
Concept
\(A\cap B={6,12}\), and both elements are in (C). Hence the difference is \(\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). \(A\cap B={6,12}\), and both elements are in (C). Hence the difference is \(\varnothing\).
Step 3
Exam Tip
\(A\cap B={6,12}\) है और ये दोनों (C) में हैं। इसलिए अंतर \(\varnothing\) है।
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\(यदि (U={1,2,\ldots,20}), (A={x:x\in U,\ x\) सम है\(}) और (B={x:x\in U,\ x\) 3 से विभाज्य है\(}) है, तो (n((A\cup B)')) कितना है\)?
\(If (U={1,2,\ldots,20}), (A={x:x\in U,\ x\) is even\(}), and (B={x:x\in U,\ x\) is divisible by \(3}), then what is (n((A\cup B)'))\)?
#sets
#union
#complement
#cardinality
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A (7)
B (13)
C (10)
D (3)
Explanation opens after your attempt
Step 1
Concept
(n(A)=10), (n(B)=6), (n\(A\cap B\)=3), so (n\(A\cup B\)=13). The complement has (20-13=7) elements.
Step 2
Why this answer is correct
The correct answer is A. (7). (n(A)=10), (n(B)=6), (n\(A\cap B\)=3), so (n\(A\cup B\)=13). The complement has (20-13=7) elements.
Step 3
Exam Tip
(n(A)=10), (n(B)=6), (n\(A\cap B\)=3), अतः (n\(A\cup B\)=13)। पूरक में (20-13=7) तत्व हैं।
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यदि \(A\subseteq B\) है, तो (A\cup\(B\setminus A\)) के बराबर क्या है?
If \(A\subseteq B\), then what is (A\cup\(B\setminus A\)) equal to?
#sets
#subset
#union
#difference
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A (B)
B (A)
C \(A\cap B\)
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Every element of (B) is either in (A) or in \(B\setminus A\). Therefore their union is (B).
Step 2
Why this answer is correct
The correct answer is A. (B). Every element of (B) is either in (A) or in \(B\setminus A\). Therefore their union is (B).
Step 3
Exam Tip
(B) के तत्व या तो (A) में हैं या \(B\setminus A\) में। इसलिए उनका संघ (B) है।
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यदि \(A\cap B=A\) और \(A\cup B=B\) है, तो सही निष्कर्ष क्या है?
If \(A\cap B=A\) and \(A\cup B=B\), then what is the correct conclusion?
#sets
#subset
#union
#intersection
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A \(A\subseteq B\)
B \(B\subseteq A\)
C (A=B')
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(A\subseteq B\)
Step 1
Concept
Both conditions show that every element of (A) is in (B). Hence \(A\subseteq B\).
Step 2
Why this answer is correct
The correct answer is A. \(A\subseteq B\). Both conditions show that every element of (A) is in (B). Hence \(A\subseteq B\).
Step 3
Exam Tip
दोनों शर्तें बताती हैं कि (A) का हर तत्व (B) में है। इसलिए \(A\subseteq B\) है।
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यदि (n(A)=30), (n(B)=24), (n\(A\setminus B\)=18) है, तो (n\(A\cup B\)) कितना है?
If (n(A)=30), (n(B)=24), and (n\(A\setminus B\)=18), then what is (n\(A\cup B\))?
#sets
#cardinality
#union
#difference
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A (42)
B (54)
C (36)
D (48)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cap B\)=30-18=12). Thus (n\(A\cup B\)=30+24-12=42).
Step 2
Why this answer is correct
The correct answer is A. (42). (n\(A\cap B\)=30-18=12). Thus (n\(A\cup B\)=30+24-12=42).
Step 3
Exam Tip
(n\(A\cap B\)=30-18=12) है। अतः (n\(A\cup B\)=30+24-12=42)।
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यदि \(A\cup B=A\cap B\) है, तो कौन-सा निष्कर्ष सदैव सत्य है?
If \(A\cup B=A\cap B\), which conclusion is always true?
#sets
#reasoning
#union
#intersection
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A (A=B)
B \(A=\varnothing\)
C \(B=\varnothing\)
D \(A\subset B'\)
Explanation opens after your attempt
Step 1
Concept
The union and intersection can be equal only when the two sets are equal. Hence (A=B).
Step 2
Why this answer is correct
The correct answer is A. (A=B). The union and intersection can be equal only when the two sets are equal. Hence (A=B).
Step 3
Exam Tip
संघ और प्रतिच्छेद तभी समान हो सकते हैं जब दोनों समुच्चय समान हों। अतः (A=B) है।
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\(यदि (A={x:x\in\mathbb{N},x\le 12}), (B={x:x\in\mathbb{N},x\) अभाज्य है\(}) और (B) को (A) तक सीमित माना गया है, तो (A\setminus B) क्या है\)?
\(If (A={x:x\in\mathbb{N},x\le 12}), (B={x:x\in\mathbb{N},x\) is prime\(}), and (B) is restricted to (A), then what is (A\setminus B)\)?
#sets
#natural-numbers
#difference
#prime
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A ({1,4,6,8,9,10,12})
B ({2,3,5,7,11})
C ({1,2,3,4,5,6})
D ({4,6,8,10,12})
Explanation opens after your attempt
Correct Answer
A. ({1,4,6,8,9,10,12})
Step 1
Concept
The prime elements in (A) are ({2,3,5,7,11}). Removing them gives ({1,4,6,8,9,10,12}).
Step 2
Why this answer is correct
The correct answer is A. ({1,4,6,8,9,10,12}). The prime elements in (A) are ({2,3,5,7,11}). Removing them gives ({1,4,6,8,9,10,12}).
Step 3
Exam Tip
(A) में अभाज्य तत्व ({2,3,5,7,11}) हैं। उन्हें हटाने पर ({1,4,6,8,9,10,12}) मिलता है।
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यदि \(A\setminus B=\varnothing\) और \(B\setminus A=\varnothing\) है, तो (A) और (B) के बीच क्या संबंध है?
If \(A\setminus B=\varnothing\) and \(B\setminus A=\varnothing\), what is the relation between (A) and (B)?
#sets
#equality
#difference
#subset
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A (A=B)
B \(A\cap B=\varnothing\)
C \(A\subset B\) पर \(A\ne B\)
D \(B\subset A\) पर \(A\ne B\)
Explanation opens after your attempt
Step 1
Concept
The first condition gives \(A\subseteq B\), and the second gives \(B\subseteq A\). Therefore (A=B).
Step 2
Why this answer is correct
The correct answer is A. (A=B). The first condition gives \(A\subseteq B\), and the second gives \(B\subseteq A\). Therefore (A=B).
Step 3
Exam Tip
पहली शर्त से \(A\subseteq B\) और दूसरी से \(B\subseteq A\) है। इसलिए (A=B) है।
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कौन-सा व्यंजक (A\setminus\(B\cap C\)) के बराबर है?
Which expression is equal to (A\setminus\(B\cap C\))?
#sets
#de-morgan
#difference
#identity
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A (\(A\setminus B\)\cup\(A\setminus C\))
B (\(A\setminus B\)\cap\(A\setminus C\))
C (\(A\cap B\)\setminus C)
D (A\cap\(B\cup C\))
Explanation opens after your attempt
Correct Answer
A. (\(A\setminus B\)\cup\(A\setminus C\))
Step 1
Concept
By the complement rule, (A\setminus\(B\cap C\)=A\cap\(B\cap C\)'). This equals (\(A\setminus B\)\cup\(A\setminus C\)).
Step 2
Why this answer is correct
The correct answer is A. (\(A\setminus B\)\cup\(A\setminus C\)). By the complement rule, (A\setminus\(B\cap C\)=A\cap\(B\cap C\)'). This equals (\(A\setminus B\)\cup\(A\setminus C\)).
Step 3
Exam Tip
पूरक नियम से (A\setminus\(B\cap C\)=A\cap\(B\cap C\)') होता है। यह (\(A\setminus B\)\cup\(A\setminus C\)) के बराबर है।
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कौन-सा व्यंजक (A\setminus\(B\cup C\)) के बराबर है?
Which expression is equal to (A\setminus\(B\cup C\))?
#sets
#de-morgan
#difference
#identity
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A (\(A\setminus B\)\cap\(A\setminus C\))
B (\(A\setminus B\)\cup\(A\setminus C\))
C (\(A\cap B\)\setminus C)
D (A\cup\(B\cap C\))
Explanation opens after your attempt
Correct Answer
A. (\(A\setminus B\)\cap\(A\setminus C\))
Step 1
Concept
Removing elements of \(B\cup C\) means being outside both (B) and (C). Hence the answer is (\(A\setminus B\)\cap\(A\setminus C\)).
Step 2
Why this answer is correct
The correct answer is A. (\(A\setminus B\)\cap\(A\setminus C\)). Removing elements of \(B\cup C\) means being outside both (B) and (C). Hence the answer is (\(A\setminus B\)\cap\(A\setminus C\)).
Step 3
Exam Tip
\(B\cup C\) के तत्व हटाने का मतलब (B) और (C) दोनों से बाहर रहना है। इसलिए उत्तर (\(A\setminus B\)\cap\(A\setminus C\)) है।
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यदि (n\(A\cup B\)=75), (n\(A\cap B\)=18) और (n(A)=46) है, तो (n(B)) कितना है?
If (n\(A\cup B\)=75), (n\(A\cap B\)=18), and (n(A)=46), then what is (n(B))?
#sets
#union
#intersection
#cardinality
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A (47)
B (29)
C (57)
D (43)
Explanation opens after your attempt
Step 1
Concept
Using the formula, (75=46+n(B)-18). Hence (n(B)=47).
Step 2
Why this answer is correct
The correct answer is A. (47). Using the formula, (75=46+n(B)-18). Hence (n(B)=47).
Step 3
Exam Tip
सूत्र से (75=46+n(B)-18) मिलेगा। इसलिए (n(B)=47) है।
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कक्षा में (64) विद्यार्थी हैं। (38) गणित, (32) भौतिकी और (20) दोनों पढ़ते हैं। ठीक एक विषय पढ़ने वाले विद्यार्थियों की संख्या कितनी है?
In a class of (64) students, (38) study Mathematics, (32) study Physics, and (20) study both. How many students study exactly one subject?
#sets
#venn
#exactly-one
#application
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A (30)
B (50)
C (44)
D (12)
Explanation opens after your attempt
Step 1
Concept
Exactly one subject (=(38-20)+(32-20)=30). In a Venn diagram, separate the common part from both sides.
Step 2
Why this answer is correct
The correct answer is A. (30). Exactly one subject (=(38-20)+(32-20)=30). In a Venn diagram, separate the common part from both sides.
Step 3
Exam Tip
ठीक एक विषय (=(38-20)+(32-20)=30) है। वेंन आरेख में साझा भाग को दोनों तरफ से अलग करें।
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एक सर्वे में (90) लोगों में से (52) चाय, (47) कॉफी और (19) दोनों पसंद करते हैं। न चाय न कॉफी पसंद करने वाले कितने हैं?
In a survey of (90) people, (52) like tea, (47) like coffee, and (19) like both. How many like neither tea nor coffee?
#sets
#union
#complement
#survey
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A (10)
B (9)
C (19)
D (28)
Explanation opens after your attempt
Step 1
Concept
(n\(T\cup C\)=52+47-19=80). Therefore the number outside is (90-80=10).
Step 2
Why this answer is correct
The correct answer is A. (10). (n\(T\cup C\)=52+47-19=80). Therefore the number outside is (90-80=10).
Step 3
Exam Tip
(n\(T\cup C\)=52+47-19=80) है। इसलिए बाहर वाले (90-80=10) हैं।
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यदि \(U={1,2,\ldots,30}\), \(A={x:x\in U,\ 2\mid x}\) और \(B={x:x\in U,\ 5\mid x}\) है, तो (n\(A\setminus B\)) कितना है?
If \(U={1,2,\ldots,30}\), \(A={x:x\in U,\ 2\mid x}\), and \(B={x:x\in U,\ 5\mid x}\), then what is (n\(A\setminus B\))?
#sets
#difference
#divisibility
#cardinality
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A (12)
B (15)
C (9)
D (3)
Explanation opens after your attempt
Step 1
Concept
There are (15) even numbers in (A), and (3) multiples of (10). Thus (n\(A\setminus B\)=15-3=12).
Step 2
Why this answer is correct
The correct answer is A. (12). There are (15) even numbers in (A), and (3) multiples of (10). Thus (n\(A\setminus B\)=15-3=12).
Step 3
Exam Tip
(A) में (15) सम संख्याएं हैं और (10) के गुणज (3) हैं। इसलिए (n\(A\setminus B\)=15-3=12)।
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यदि \(A={x:x\in\mathbb{R},x^2-5x+6=0}\) और \(B={x:x\in\mathbb{R},x^2-4x+3=0}\) है, तो \(A\cap B\) क्या है?
If \(A={x:x\in\mathbb{R},x^2-5x+6=0}\) and \(B={x:x\in\mathbb{R},x^2-4x+3=0}\), then what is \(A\cap B\)?
#sets
#set-builder
#intersection
#quadratic
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A ({3})
B ({1,2,3})
C ({2})
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The first equation gives \(A=\{2,3\}\), and the second gives \(B=\{1,3\}\). The common element is ({3}).
Step 2
Why this answer is correct
The correct answer is A. ({3}). The first equation gives \(A=\{2,3\}\), and the second gives \(B=\{1,3\}\). The common element is ({3}).
Step 3
Exam Tip
पहले समीकरण से \(A=\{2,3\}\) और दूसरे से \(B=\{1,3\}\) है। समान तत्व ({3}) है।
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यदि \(A={x:x\in\mathbb{R},x^2\le 16}\) और \(B={x:x\in\mathbb{R},x>1}\) है, तो \(A\cap B\) क्या है?
If \(A={x:x\in\mathbb{R},x^2\le 16}\) and \(B={x:x\in\mathbb{R},x>1}\), then what is \(A\cap B\)?
#sets
#inequalities
#intersection
#intervals
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A ((1,4])
B ([1,4])
C ([-4,1])
D ((-4,4))
Explanation opens after your attempt
Correct Answer
A. ((1,4])
Step 1
Concept
From \(x^2\le 16\), (A=[-4,4]). With (x>1), the common part is ((1,4]).
Step 2
Why this answer is correct
The correct answer is A. ((1,4]). From \(x^2\le 16\), (A=[-4,4]). With (x>1), the common part is ((1,4]).
Step 3
Exam Tip
\(x^2\le 16\) से (A=[-4,4]) है। (x>1) के साथ साझा भाग ((1,4]) है।
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यदि \(A={x:x\in\mathbb{R},-1<x\le 5}\) और \(B={x:x\in\mathbb{R},2\le x<7}\) है, तो \(A\setminus B\) क्या है?
If \(A={x:x\in\mathbb{R},-1<x\le 5}\) and \(B={x:x\in\mathbb{R},2\le x<7}\), then what is \(A\setminus B\)?
#sets
#intervals
#difference
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A ((-1,2))
B ((-1,2])
C ([2,5])
D ((5,7))
Explanation opens after your attempt
Correct Answer
A. ((-1,2))
Step 1
Concept
Since (2) is included in (B), (2) and the common part after it are removed from (A). The remaining part is ((-1,2)).
Step 2
Why this answer is correct
The correct answer is A. ((-1,2)). Since (2) is included in (B), (2) and the common part after it are removed from (A). The remaining part is ((-1,2)).
Step 3
Exam Tip
(B) में (2) शामिल है, इसलिए (A) से (2) और उसके बाद का साझा भाग हटेगा। बचा भाग ((-1,2)) है।
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यदि \(A=\{1,2,3,4,5\}\), \(B=\{2,4,6\}\) और \(C=\{1,4,7\}\) है, तो (A\cap\(B\cup C\)) क्या है?
If \(A=\{1,2,3,4,5\}\), \(B=\{2,4,6\}\), and \(C=\{1,4,7\}\), then what is (A\cap\(B\cup C\))?
#sets
#union
#intersection
#finite-sets
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A ({1,2,4})
B ({2,4,6,7})
C ({1,4})
D ({3,5})
Explanation opens after your attempt
Correct Answer
A. ({1,2,4})
Step 1
Concept
\(B\cup C={1,2,4,6,7}\). Its common part with (A) is ({1,2,4}).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,4}). \(B\cup C={1,2,4,6,7}\). Its common part with (A) is ({1,2,4}).
Step 3
Exam Tip
\(B\cup C={1,2,4,6,7}\) है। इसका (A) से साझा भाग ({1,2,4}) है।
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यदि \(A=\{1,3,5,7,9\}\), \(B=\{3,6,9\}\) और \(C=\{1,2,3,4\}\) है, तो (\(A\cup B\)\setminus C) क्या है?
If \(A=\{1,3,5,7,9\}\), \(B=\{3,6,9\}\), and \(C=\{1,2,3,4\}\), then what is (\(A\cup B\)\setminus C)?
#sets
#union
#difference
#finite-sets
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A ({5,6,7,9})
B ({1,3})
C ({6,9})
D ({5,7})
Explanation opens after your attempt
Correct Answer
A. ({5,6,7,9})
Step 1
Concept
\(A\cup B={1,3,5,6,7,9}\). Removing elements of (C) gives ({5,6,7,9}).
Step 2
Why this answer is correct
The correct answer is A. ({5,6,7,9}). \(A\cup B={1,3,5,6,7,9}\). Removing elements of (C) gives ({5,6,7,9}).
Step 3
Exam Tip
\(A\cup B={1,3,5,6,7,9}\) है। (C) के तत्व हटाने पर ({5,6,7,9}) मिलता है।
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यदि \(A\setminus B=A\) है, तो कौन-सा कथन सदैव सत्य है?
If \(A\setminus B=A\), which statement is always true?
#sets
#difference
#disjoint
#reasoning
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A \(A\cap B=\varnothing\)
B \(A\subseteq B\)
C \(B\subseteq A\)
D \(A\cup B=A\)
Explanation opens after your attempt
Correct Answer
A. \(A\cap B=\varnothing\)
Step 1
Concept
Removing (B) from (A) still leaves (A), so (A) and (B) have no common element. Hence \(A\cap B=\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(A\cap B=\varnothing\). Removing (B) from (A) still leaves (A), so (A) and (B) have no common element. Hence \(A\cap B=\varnothing\).
Step 3
Exam Tip
(A) से (B) हटाने पर भी (A) बच रहा है, इसलिए (A) और (B) में कोई साझा तत्व नहीं है। अतः \(A\cap B=\varnothing\) है।
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यदि \(A\cap B=\varnothing\), (n(A)=21) और (n(B)=17) है, तो (n\(A\cup B\)) कितना होगा?
If \(A\cap B=\varnothing\), (n(A)=21), and (n(B)=17), then what is (n\(A\cup B\))?
#sets
#disjoint
#union
#cardinality
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A (38)
B (21)
C (17)
D (4)
Explanation opens after your attempt
Step 1
Concept
Disjoint sets have no common element. Therefore (n\(A\cup B\)=21+17=38).
Step 2
Why this answer is correct
The correct answer is A. (38). Disjoint sets have no common element. Therefore (n\(A\cup B\)=21+17=38).
Step 3
Exam Tip
असंबद्ध समुच्चयों में कोई साझा तत्व नहीं होता। इसलिए (n\(A\cup B\)=21+17=38)।
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यदि \(A\setminus B={2,5}\), \(B\setminus A={7}\) और \(A\cap B={1,3}\) है, तो \(A\cup B\) क्या है?
If \(A\setminus B={2,5}\), \(B\setminus A={7}\), and \(A\cap B={1,3}\), then what is \(A\cup B\)?
#sets
#venn-parts
#union
#difference
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A ({1,2,3,5,7})
B ({2,5,7})
C ({1,3})
D ({1,2,3})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,5,7})
Step 1
Concept
The union is formed from the three disjoint parts \(A\setminus B\), \(B\setminus A\), and \(A\cap B\). Hence the answer is ({1,2,3,5,7}).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,5,7}). The union is formed from the three disjoint parts \(A\setminus B\), \(B\setminus A\), and \(A\cap B\). Hence the answer is ({1,2,3,5,7}).
Step 3
Exam Tip
संघ तीन असंबद्ध भागों \(A\setminus B\), \(B\setminus A\) और \(A\cap B\) से बनता है। इसलिए उत्तर ({1,2,3,5,7}) है।
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यदि (n\(A\setminus B\)=12), (n\(B\setminus A\)=9) और (n\(A\cap B\)=6) है, तो (n\(A\cup B\)) कितना है?
If (n\(A\setminus B\)=12), (n\(B\setminus A\)=9), and (n\(A\cap B\)=6), then what is (n\(A\cup B\))?
#sets
#venn-parts
#cardinality
#union
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A (27)
B (21)
C (18)
D (15)
Explanation opens after your attempt
Step 1
Concept
The union is the sum of these three disjoint parts. Therefore (n\(A\cup B\)=12+9+6=27).
Step 2
Why this answer is correct
The correct answer is A. (27). The union is the sum of these three disjoint parts. Therefore (n\(A\cup B\)=12+9+6=27).
Step 3
Exam Tip
संघ इन तीन असंबद्ध भागों का योग है। इसलिए (n\(A\cup B\)=12+9+6=27)।
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यदि \(A\cup B=A\) है, तो \(B\setminus A\) क्या होगा?
If \(A\cup B=A\), then what is \(B\setminus A\)?
#sets
#subset
#union
#difference
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A \(\varnothing\)
B (B)
C (A)
D \(A\cap B\)
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\)
Step 1
Concept
From \(A\cup B=A\), we get \(B\subseteq A\). Thus (B) has no element outside (A).
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). From \(A\cup B=A\), we get \(B\subseteq A\). Thus (B) has no element outside (A).
Step 3
Exam Tip
\(A\cup B=A\) से \(B\subseteq A\) मिलता है। इसलिए (B) में (A) के बाहर कोई तत्व नहीं है।
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यदि \(A\cap B=B\) है, तो \(A\setminus B\) के बारे में कौन-सा कथन निश्चित रूप से सही नहीं है?
If \(A\cap B=B\), which statement about \(A\setminus B\) is not definitely true?
#sets
#reasoning
#intersection
#difference
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A \(A\setminus B=\varnothing\)
B \(A\setminus B\subseteq A\)
C (\(A\setminus B\)\cap B=\varnothing)
D \(A\setminus B=A\cap B'\)
Explanation opens after your attempt
Correct Answer
A. \(A\setminus B=\varnothing\)
Step 1
Concept
\(A\cap B=B\) gives \(B\subseteq A\), but \(A\setminus B\) may or may not be empty. The other statements are always true.
Step 2
Why this answer is correct
The correct answer is A. \(A\setminus B=\varnothing\). \(A\cap B=B\) gives \(B\subseteq A\), but \(A\setminus B\) may or may not be empty. The other statements are always true.
Step 3
Exam Tip
\(A\cap B=B\) से \(B\subseteq A\) मिलता है, पर \(A\setminus B\) खाली भी हो सकता है और नहीं भी। बाकी कथन सदैव सत्य हैं।
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यदि \(U={1,2,\ldots,50}\), \(A={x:x\in U,\ 4\mid x}\) और \(B={x:x\in U,\ 6\mid x}\) है, तो (n\(A\cap B\)) कितना है?
If \(U={1,2,\ldots,50}\), \(A={x:x\in U,\ 4\mid x}\), and \(B={x:x\in U,\ 6\mid x}\), then what is (n\(A\cap B\))?
#sets
#intersection
#divisibility
#lcm
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A (4)
B (8)
C (12)
D (2)
Explanation opens after your attempt
Step 1
Concept
Common elements are multiples of (\operatorname{lcm}(4,6)=12). Up to (50), they are (12,24,36,48), so there are (4) elements.
Step 2
Why this answer is correct
The correct answer is A. (4). Common elements are multiples of (\operatorname{lcm}(4,6)=12). Up to (50), they are (12,24,36,48), so there are (4) elements.
Step 3
Exam Tip
साझा तत्व (\operatorname{lcm}(4,6)=12) के गुणज होंगे। (50) तक (12,24,36,48) यानी (4) तत्व हैं।
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यदि \(A={x:x\in\mathbb{Z},|x|\le 4}\) और \(B={x:x\in\mathbb{Z},x^2-2x-3=0}\) है, तो \(A\setminus B\) में कितने तत्व हैं?
If \(A={x:x\in\mathbb{Z},|x|\le 4}\) and \(B={x:x\in\mathbb{Z},x^2-2x-3=0}\), then how many elements are in \(A\setminus B\)?
#sets
#absolute-value
#difference
#integers
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A (7)
B (9)
C (2)
D (6)
Explanation opens after your attempt
Step 1
Concept
(A) has (9) elements, and \(B=\{-1,3\}\). Therefore \(A\setminus B\) has (9-2=7) elements.
Step 2
Why this answer is correct
The correct answer is A. (7). (A) has (9) elements, and \(B=\{-1,3\}\). Therefore \(A\setminus B\) has (9-2=7) elements.
Step 3
Exam Tip
(A) में (9) तत्व हैं और \(B=\{-1,3\}\) है। इसलिए \(A\setminus B\) में (9-2=7) तत्व हैं।
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यदि \(A\triangle B\) को (\(A\setminus B\)\cup\(B\setminus A\)) से परिभाषित किया जाए और (n\(A\cup B\)=40), (n\(A\cap B\)=13) हो, तो (n\(A\triangle B\)) कितना है?
If \(A\triangle B\) is defined as (\(A\setminus B\)\cup\(B\setminus A\)) and (n\(A\cup B\)=40), (n\(A\cap B\)=13), then what is (n\(A\triangle B\))?
#sets
#symmetric-difference
#union
#intersection
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A (27)
B (53)
C (13)
D (40)
Explanation opens after your attempt
Step 1
Concept
\(A\triangle B\) removes the common part from the union. Therefore (n\(A\triangle B\)=40-13=27).
Step 2
Why this answer is correct
The correct answer is A. (27). \(A\triangle B\) removes the common part from the union. Therefore (n\(A\triangle B\)=40-13=27).
Step 3
Exam Tip
\(A\triangle B\) संघ में से साझा भाग हटाता है। इसलिए (n\(A\triangle B\)=40-13=27)।
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यदि \(A=\{a,b,c,d\}\) और \(B=\{c,d,e\}\) है, तो (\mathcal{P}\(A\cap B\)) में कितने तत्व होंगे?
If \(A=\{a,b,c,d\}\) and \(B=\{c,d,e\}\), then how many elements are in (\mathcal{P}\(A\cap B\))?
#sets
#power-set
#intersection
#cardinality
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A (4)
B (2)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(A\cap B={c,d}\) has (2) elements. Hence (\mathcal{P}\(A\cap B\)) has \(2^2=4\) elements.
Step 2
Why this answer is correct
The correct answer is A. (4). \(A\cap B={c,d}\) has (2) elements. Hence (\mathcal{P}\(A\cap B\)) has \(2^2=4\) elements.
Step 3
Exam Tip
\(A\cap B={c,d}\) में (2) तत्व हैं। इसलिए (\mathcal{P}\(A\cap B\)) में \(2^2=4\) तत्व होंगे।
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यदि \(A\subseteq U\) और \(B\subseteq U\), तो (\(A\setminus B\)') किसके बराबर है?
If \(A\subseteq U\) and \(B\subseteq U\), then (\(A\setminus B\)') is equal to what?
#sets
#complement
#difference
#de-morgan
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A \(A'\cup B\)
B \(A'\cap B\)
C \(A\cup B'\)
D \(A\cap B\)
Explanation opens after your attempt
Correct Answer
A. \(A'\cup B\)
Step 1
Concept
\(A\setminus B=A\cap B'\). Its complement is (\(A\cap B'\)'=A'\cup B).
Step 2
Why this answer is correct
The correct answer is A. \(A'\cup B\). \(A\setminus B=A\cap B'\). Its complement is (\(A\cap B'\)'=A'\cup B).
Step 3
Exam Tip
\(A\setminus B=A\cap B'\) है। इसका पूरक (\(A\cap B'\)'=A'\cup B) होगा।
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यदि (A) और (B) सीमित समुच्चय हैं, तो (n\(A\setminus B\)) के लिए सही सूत्र कौन-सा है?
If (A) and (B) are finite sets, which is the correct formula for (n\(A\setminus B\))?
#sets
#difference
#formula
#cardinality
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A (n(A)-n\(A\cap B\))
B (n(A)+n(B))
C (n\(A\cup B\)-n(B))
D (n(B)-n\(A\cap B\))
Explanation opens after your attempt
Correct Answer
A. (n(A)-n\(A\cap B\))
Step 1
Concept
\(A\setminus B\) contains elements of (A) that are not in the common part. Hence (n\(A\setminus B\)=n(A)-n\(A\cap B\)).
Step 2
Why this answer is correct
The correct answer is A. (n(A)-n\(A\cap B\)). \(A\setminus B\) contains elements of (A) that are not in the common part. Hence (n\(A\setminus B\)=n(A)-n\(A\cap B\)).
Step 3
Exam Tip
\(A\setminus B\) में (A) के वे तत्व हैं जो साझा भाग में नहीं हैं। इसलिए (n\(A\setminus B\)=n(A)-n\(A\cap B\))।
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यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{2,3,5,7\}\), \(C=\{3,4,5,8\}\) है, तो (\(A\setminus B\)\cap C) क्या है?
If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,3,5,7\}\), and \(C=\{3,4,5,8\}\), then what is (\(A\setminus B\)\cap C)?
#sets
#difference
#intersection
#finite-sets
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A ({4})
B ({3,5})
C ({1,4,6})
D ({4,8})
Explanation opens after your attempt
Step 1
Concept
\(A\setminus B={1,4,6}\). Its only common element with (C) is (4).
Step 2
Why this answer is correct
The correct answer is A. ({4}). \(A\setminus B={1,4,6}\). Its only common element with (C) is (4).
Step 3
Exam Tip
\(A\setminus B={1,4,6}\) है। इसका (C) से साझा तत्व केवल (4) है।
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यदि (A\cap\(B\cup C\)=\(A\cap B\)\cup\(A\cap C\)) है, तो यह कौन-सा नियम है?
If (A\cap\(B\cup C\)=\(A\cap B\)\cup\(A\cap C\)), which law is this?
#sets
#identity
#distributive-law
#union-intersection
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A वितरण नियम / Distributive law
B क्रमविनिमेय नियम / Commutative law
C सहचर नियम / Associative law
D पूरक नियम / Complement law
Explanation opens after your attempt
Correct Answer
A. वितरण नियम / Distributive law
Step 1
Concept
This is the distributive law of intersection over union. In identity questions, observe the position of symbols carefully.
Step 2
Why this answer is correct
The correct answer is A. वितरण नियम / Distributive law. This is the distributive law of intersection over union. In identity questions, observe the position of symbols carefully.
Step 3
Exam Tip
यह प्रतिच्छेद का संघ पर वितरण है। पहचान वाले प्रश्नों में प्रतीकों की स्थिति ध्यान से देखें।
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यदि (A\cup\(B\cap C\)=\(A\cup B\)\cap\(A\cup C\)) है, तो यह कौन-सा नियम है?
If (A\cup\(B\cap C\)=\(A\cup B\)\cap\(A\cup C\)), which law is this?
#sets
#identity
#distributive-law
#operations
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A वितरण नियम / Distributive law
B डी मॉर्गन नियम / De Morgan law
C अवशोषण नियम / Absorption law
D सर्वसमिका नियम / Identity law
Explanation opens after your attempt
Correct Answer
A. वितरण नियम / Distributive law
Step 1
Concept
This is the distributive law of union over intersection. Remember both forms of the distributive law separately.
Step 2
Why this answer is correct
The correct answer is A. वितरण नियम / Distributive law. This is the distributive law of union over intersection. Remember both forms of the distributive law separately.
Step 3
Exam Tip
यह संघ का प्रतिच्छेद पर वितरण है। दोनों वितरण नियम अलग-अलग रूपों में याद रखें।
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यदि (A\cup\(A\cap B\)=A) है, तो यह कौन-सा नियम दर्शाता है?
If (A\cup\(A\cap B\)=A), which law does this represent?
#sets
#absorption-law
#union
#intersection
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A अवशोषण नियम / Absorption law
B वितरण नियम / Distributive law
C डी मॉर्गन नियम / De Morgan law
D रिक्त समुच्चय नियम / Empty set law
Explanation opens after your attempt
Correct Answer
A. अवशोषण नियम / Absorption law
Step 1
Concept
This is a form of the absorption law. Adding \(A\cap B\) to (A) still gives (A).
Step 2
Why this answer is correct
The correct answer is A. अवशोषण नियम / Absorption law. This is a form of the absorption law. Adding \(A\cap B\) to (A) still gives (A).
Step 3
Exam Tip
यह अवशोषण नियम का रूप है। (A) के साथ \(A\cap B\) जोड़ने से (A) ही रहता है।
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यदि (A\cap\(A\cup B\)=A) है, तो यह कौन-सा नियम दर्शाता है?
If (A\cap\(A\cup B\)=A), which law does this represent?
#sets
#absorption-law
#intersection
#union
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A अवशोषण नियम / Absorption law
B क्रमविनिमेय नियम / Commutative law
C सहचर नियम / Associative law
D पूरक नियम / Complement law
Explanation opens after your attempt
Correct Answer
A. अवशोषण नियम / Absorption law
Step 1
Concept
This is also the absorption law. (A) is already contained inside \(A\cup B\).
Step 2
Why this answer is correct
The correct answer is A. अवशोषण नियम / Absorption law. This is also the absorption law. (A) is already contained inside \(A\cup B\).
Step 3
Exam Tip
यह भी अवशोषण नियम है। \(A\cup B\) के भीतर (A) पहले से शामिल है।
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कौन-सा विकल्प \(A\cap B'\) के बराबर है?
Which option is equal to \(A\cap B'\)?
#sets
#complement
#difference
#identity
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A \(A\setminus B\)
B \(B\setminus A\)
C \(A\cup B\)
D \(A'\cap B\)
Explanation opens after your attempt
Correct Answer
A. \(A\setminus B\)
Step 1
Concept
\(A\cap B'\) means being in (A) and not being in (B). This is exactly \(A\setminus B\).
Step 2
Why this answer is correct
The correct answer is A. \(A\setminus B\). \(A\cap B'\) means being in (A) and not being in (B). This is exactly \(A\setminus B\).
Step 3
Exam Tip
\(A\cap B'\) का अर्थ है (A) में रहना और (B) में न रहना। यही \(A\setminus B\) है।
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यदि \(A={x:x\in\mathbb{Z},-5\le x<3}\) और \(B={x:x\in\mathbb{Z},-2<x\le 6}\) है, तो \(A\cup B\) क्या है?
If \(A={x:x\in\mathbb{Z},-5\le x<3}\) and \(B={x:x\in\mathbb{Z},-2<x\le 6}\), then what is \(A\cup B\)?
#sets
#integers
#union
#intervals
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A ({-5,-4,-3,-2,-1,0,1,2,3,4,5,6})
B ({-1,0,1,2})
C ({-5,-4,-3,-2})
D ({3,4,5,6})
Explanation opens after your attempt
Correct Answer
A. ({-5,-4,-3,-2,-1,0,1,2,3,4,5,6})
Step 1
Concept
The two integer intervals are connected with no gap. Therefore the union is all integers from (-5) to (6).
Step 2
Why this answer is correct
The correct answer is A. ({-5,-4,-3,-2,-1,0,1,2,3,4,5,6}). The two integer intervals are connected with no gap. Therefore the union is all integers from (-5) to (6).
Step 3
Exam Tip
दोनों पूर्णांक अंतराल जुड़े हुए हैं और बीच में कोई खाली स्थान नहीं है। इसलिए संघ (-5) से (6) तक के सभी पूर्णांक हैं।
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यदि \(A\subseteq B\subseteq C\) है, तो (A\cap\(C\setminus B\)) क्या होगा?
If \(A\subseteq B\subseteq C\), then what is (A\cap\(C\setminus B\))?
#sets
#subset
#difference
#intersection
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A \(\varnothing\)
B (A)
C \(C\setminus A\)
D \(B\setminus A\)
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Correct Answer
A. \(\varnothing\)
Step 1
Concept
\(C\setminus B\) contains elements outside (B). Since \(A\subseteq B\), no element of (A) can be there.
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). \(C\setminus B\) contains elements outside (B). Since \(A\subseteq B\), no element of (A) can be there.
Step 3
Exam Tip
\(C\setminus B\) में (B) से बाहर के तत्व होते हैं। \(A\subseteq B\) होने से (A) का कोई तत्व वहां नहीं होगा।
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यदि \(A\cap B\ne\varnothing\) और \(A\setminus B=\varnothing\) है, तो कौन-सा निष्कर्ष सही है?
If \(A\cap B\ne\varnothing\) and \(A\setminus B=\varnothing\), which conclusion is correct?
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#reasoning
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#difference
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A \(A\subseteq B\) और \(A\ne\varnothing\)
B \(B\subseteq A\) और \(B=\varnothing\)
C \(A\cap B=\varnothing\)
D \(A\cup B=A\)
Explanation opens after your attempt
Correct Answer
A. \(A\subseteq B\) और \(A\ne\varnothing\)
Step 1
Concept
\(A\setminus B=\varnothing\) gives \(A\subseteq B\). \(A\cap B\ne\varnothing\) shows that (A) is not empty.
Step 2
Why this answer is correct
The correct answer is A. \(A\subseteq B\) और \(A\ne\varnothing\). \(A\setminus B=\varnothing\) gives \(A\subseteq B\). \(A\cap B\ne\varnothing\) shows that (A) is not empty.
Step 3
Exam Tip
\(A\setminus B=\varnothing\) से \(A\subseteq B\) है। \(A\cap B\ne\varnothing\) बताता है कि (A) खाली नहीं है।
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यदि (n(A)=18), (n(B)=25) और (n\(A\cup B\)=25) है, तो (n\(A\setminus B\)) कितना है?
If (n(A)=18), (n(B)=25), and (n\(A\cup B\)=25), then what is (n\(A\setminus B\))?
#sets
#cardinality
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#difference
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A (0)
B (7)
C (18)
D (25)
Explanation opens after your attempt
Step 1
Concept
Since (n\(A\cup B\)=n(B)), we have \(A\subseteq B\). Hence \(A\setminus B=\varnothing\) and the number is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). Since (n\(A\cup B\)=n(B)), we have \(A\subseteq B\). Hence \(A\setminus B=\varnothing\) and the number is (0).
Step 3
Exam Tip
(n\(A\cup B\)=n(B)) से \(A\subseteq B\) है। इसलिए \(A\setminus B=\varnothing\) और संख्या (0) है।
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यदि \(A={x:x\in\mathbb{R},0\le x<5}\) और \(B={x:x\in\mathbb{R},3<x\le 8}\) है, तो (\(A\cup B\)\setminus\(A\cap B\)) क्या है?
If \(A={x:x\in\mathbb{R},0\le x<5}\) and \(B={x:x\in\mathbb{R},3<x\le 8}\), then what is (\(A\cup B\)\setminus\(A\cap B\))?
#sets
#intervals
#union
#intersection
#difference
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A \([0,3]\cup[5,8]\)
B ((3,5))
C ([0,8])
D ((5,8])
Explanation opens after your attempt
Correct Answer
A. \([0,3]\cup[5,8]\)
Step 1
Concept
\(A\cap B=(3,5)\) and \(A\cup B=[0,8]\). Removing the common part leaves \([0,3]\cup[5,8]\).
Step 2
Why this answer is correct
The correct answer is A. \([0,3]\cup[5,8]\). \(A\cap B=(3,5)\) and \(A\cup B=[0,8]\). Removing the common part leaves \([0,3]\cup[5,8]\).
Step 3
Exam Tip
\(A\cap B=(3,5)\) और \(A\cup B=[0,8]\) है। साझा भाग हटाने पर \([0,3]\cup[5,8]\) बचता है।
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यदि (n\(A\cup B\cup C\)=86), (n(A)=38), (n(B)=34), (n(C)=31), (n\(A\cap B\)=12), (n\(B\cap C\)=10), (n\(C\cap A\)=9) है, तो (n\(A\cap B\cap C\)) कितना है?
If (n\(A\cup B\cup C\)=86), (n(A)=38), (n(B)=34), (n(C)=31), (n\(A\cap B\)=12), (n\(B\cap C\)=10), (n\(C\cap A\)=9), then what is (n\(A\cap B\cap C\))?
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#three-sets
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#intersection
#cardinality
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A (14)
B (4)
C (10)
D (18)
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Step 1
Concept
Use the formula for three sets: (86=38+34+31-12-10-9+x). This gives (x=14).
Step 2
Why this answer is correct
The correct answer is A. (14). Use the formula for three sets: (86=38+34+31-12-10-9+x). This gives (x=14).
Step 3
Exam Tip
तीन समुच्चयों का सूत्र लगाएं: (86=38+34+31-12-10-9+x)। इससे (x=14) मिलता है।
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यदि \(U={1,2,\ldots,40}\), \(A={x:x\in U,\ 2\mid x}\), \(B={x:x\in U,\ 3\mid x}\) और \(C={x:x\in U,\ 5\mid x}\) है, तो (n\(A\cup B\cup C\)) कितना है?
If \(U={1,2,\ldots,40}\), \(A={x:x\in U,\ 2\mid x}\), \(B={x:x\in U,\ 3\mid x}\), and \(C={x:x\in U,\ 5\mid x}\), then what is (n\(A\cup B\cup C\))?
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#three-sets
#union
#divisibility
#cardinality
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A (30)
B (31)
C (29)
D (28)
Explanation opens after your attempt
Step 1
Concept
Using the three-set formula gives (20+13+8-6-4-2+1=30). In exams, subtract pairwise intersections and add the triple intersection.
Step 2
Why this answer is correct
The correct answer is A. (30). Using the three-set formula gives (20+13+8-6-4-2+1=30). In exams, subtract pairwise intersections and add the triple intersection.
Step 3
Exam Tip
तीन समुच्चयों के सूत्र से (20+13+8-6-4-2+1=30) मिलता है। परीक्षा में युग्म प्रतिच्छेद घटाकर त्रिक प्रतिच्छेद जोड़ें।
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यदि (n\(A\cup B\)=70), (n\(A\setminus B\)=22) और (n\(B\setminus A\)=31) है, तो (n\(A\cap B\)) कितना होगा?
If (n\(A\cup B\)=70), (n\(A\setminus B\)=22), and (n\(B\setminus A\)=31), then what is (n\(A\cap B\))?
#sets
#venn-parts
#intersection
#difference
#cardinality
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A (17)
B (39)
C (53)
D (14)
Explanation opens after your attempt
Step 1
Concept
The union is made of three disjoint parts \(A\setminus B\), \(B\setminus A\), and \(A\cap B\). Therefore (n\(A\cap B\)=70-22-31=17).
Step 2
Why this answer is correct
The correct answer is A. (17). The union is made of three disjoint parts \(A\setminus B\), \(B\setminus A\), and \(A\cap B\). Therefore (n\(A\cap B\)=70-22-31=17).
Step 3
Exam Tip
संघ तीन असंबद्ध भागों \(A\setminus B\), \(B\setminus A\) और \(A\cap B\) से बनता है। इसलिए (n\(A\cap B\)=70-22-31=17)।
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