यदि \(U=\{1,2,3,4,5,6,7,8,9,10,11,12\}\), \(A=\{2,4,6,8,10,12\}\) और \(B=\{3,6,9,12\}\) है, तो \(A^c\cap B^c\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9,10,11,12\}\), \(A=\{2,4,6,8,10,12\}\), and \(B=\{3,6,9,12\}\), what is \(A^c\cap B^c\)?
#sets
#complement
#de_morgan
#finite_sets
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A ({1,5,7,11})
B ({6,12})
C ({2,3,4,6,8,9,10,12}) / ({2,3,4,6,8,10,12})
D ({1,2,3,5,7,11})
Explanation opens after your attempt
Correct Answer
A. ({1,5,7,11})
Step 1
Concept
(A^c\cap B^c=\(A\cup B\)^c). Since \(A\cup B={2,3,4,6,8,9,10,12}\), the remaining elements are the answer.
Step 2
Why this answer is correct
The correct answer is A. ({1,5,7,11}). (A^c\cap B^c=\(A\cup B\)^c). Since \(A\cup B={2,3,4,6,8,9,10,12}\), the remaining elements are the answer.
Step 3
Exam Tip
(A^c\cap B^c=\(A\cup B\)^c) होता है। \(A\cup B={2,3,4,6,8,9,10,12}\), इसलिए बचे तत्व उत्तर हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4,5\}\) और \(B=\{4,5,6,7\}\) है, तो \(A^c\cup B^c\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4,5\}\), and \(B=\{4,5,6,7\}\), what is \(A^c\cup B^c\)?
#sets
#complement
#de_morgan
#union
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A ({1,2,3,6,7,8,9,10})
B ({4,5})
C ({8,9,10})
D ({1,2,3})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,6,7,8,9,10})
Step 1
Concept
(A^c\cup B^c=\(A\cap B\)^c). Since \(A\cap B={4,5}\), remove it from (U) to get the answer.
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,6,7,8,9,10}). (A^c\cup B^c=\(A\cap B\)^c). Since \(A\cap B={4,5}\), remove it from (U) to get the answer.
Step 3
Exam Tip
(A^c\cup B^c=\(A\cap B\)^c) होता है। \(A\cap B={4,5}\), इसलिए (U) से इसे हटाने पर उत्तर मिलता है।
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\(यदि (U={x:x\in\mathbb{N},1\le x\le 20}) और (A={x:x\) अभाज्य संख्या है\(}) है, तो (A^c) में कितने तत्व होंगे\)?
\(If (U={x:x\in\mathbb{N},1\le x\le 20}) and (A={x:x\) is a prime number\(}), how many elements are in (A^c)\)?
#sets
#complement
#cardinality
#prime_numbers
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A (12)
B (8)
C (10)
D (20)
Explanation opens after your attempt
Step 1
Concept
There are (8) primes from (1) to (20), so (n\(A^c\)=20-8=12). Do not treat (1) as prime.
Step 2
Why this answer is correct
The correct answer is A. (12). There are (8) primes from (1) to (20), so (n\(A^c\)=20-8=12). Do not treat (1) as prime.
Step 3
Exam Tip
(1) से (20) तक (8) अभाज्य संख्याएं हैं, इसलिए (n\(A^c\)=20-8=12)। (1) को अभाज्य न मानें।
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यदि \(U={x:x\in\mathbb{Z},-4\le x\le 4}\) और \(A={x:x^2\le 4}\) है, तो \(A^c\) क्या होगा?
If \(U={x:x\in\mathbb{Z},-4\le x\le 4}\) and \(A={x:x^2\le 4}\), what is \(A^c\)?
#sets
#complement
#integers
#inequality
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A ({-4,-3,3,4})
B ({-2,-1,0,1,2})
C ({-4,-2,0,2,4})
D ({-3,-2,-1,0,1,2,3})
Explanation opens after your attempt
Correct Answer
A. ({-4,-3,3,4})
Step 1
Concept
From \(x^2\le 4\), \(A=\{-2,-1,0,1,2\}\). The remaining elements of (U) form \(A^c\).
Step 2
Why this answer is correct
The correct answer is A. ({-4,-3,3,4}). From \(x^2\le 4\), \(A=\{-2,-1,0,1,2\}\). The remaining elements of (U) form \(A^c\).
Step 3
Exam Tip
\(x^2\le 4\) से \(A=\{-2,-1,0,1,2\}\) मिलता है। (U) के बाकी तत्व \(A^c\) बनाते हैं।
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यदि (U=[-2,6]) और (A=(1,4]) है, तो \(A^c\) क्या होगा?
If (U=[-2,6]) and (A=(1,4]), what is \(A^c\)?
#sets
#complement
#intervals
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A ([-2,1]\cup(4,6])
B ([-2,1)\cup[4,6])
C ((1,4])
D ([-2,6])
Explanation opens after your attempt
Correct Answer
A. ([-2,1]\cup(4,6])
Step 1
Concept
(1) is not in (A), so it is included in the complement. (4) is in (A), so the complement starts after (4).
Step 2
Why this answer is correct
The correct answer is A. ([-2,1]\cup(4,6]). (1) is not in (A), so it is included in the complement. (4) is in (A), so the complement starts after (4).
Step 3
Exam Tip
(1) (A) में नहीं है, इसलिए पूरक में शामिल होगा। (4) (A) में है, इसलिए पूरक (4) के बाद शुरू होगा।
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यदि (U=(-5,5]) और (A=[-1,3)) है, तो \(A^c\) क्या होगा?
If (U=(-5,5]) and (A=[-1,3)), what is \(A^c\)?
#sets
#complement
#interval_complement
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A \((-5,-1)\cup[3,5]\)
B ((-5,-1]\cup(3,5])
C ([-1,3))
D ((-5,5])
Explanation opens after your attempt
Correct Answer
A. \((-5,-1)\cup[3,5]\)
Step 1
Concept
(-1) is in (A), so it is not in the complement. (3) is not in (A), so it is included in the complement.
Step 2
Why this answer is correct
The correct answer is A. \((-5,-1)\cup[3,5]\). (-1) is in (A), so it is not in the complement. (3) is not in (A), so it is included in the complement.
Step 3
Exam Tip
(-1) (A) में है, इसलिए पूरक में नहीं आएगा। (3) (A) में नहीं है, इसलिए पूरक में शामिल होगा।
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यदि \(A\subseteq B\subseteq U\) है, तो निम्न में से कौन सा कथन हमेशा सही है?
If \(A\subseteq B\subseteq U\), which of the following is always true?
#sets
#complement
#subset_property
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A \(B^c\subseteq A^c\)
B \(A^c\subseteq B^c\)
C \(A^c=B^c\)
D \(A^c\cap B^c=U\)
Explanation opens after your attempt
Correct Answer
A. \(B^c\subseteq A^c\)
Step 1
Concept
The order of inclusion reverses after taking complements. Thus \(A\subseteq B\) gives \(B^c\subseteq A^c\).
Step 2
Why this answer is correct
The correct answer is A. \(B^c\subseteq A^c\). The order of inclusion reverses after taking complements. Thus \(A\subseteq B\) gives \(B^c\subseteq A^c\).
Step 3
Exam Tip
पूरक लेने पर समावेशन का क्रम उलट जाता है। इसलिए \(A\subseteq B\) से \(B^c\subseteq A^c\) मिलता है।
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यदि \(A^c\subseteq B^c\) है, तो कौन सा निष्कर्ष सही है?
If \(A^c\subseteq B^c\), which conclusion is correct?
#sets
#complement
#reverse_inclusion
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A \(B\subseteq A\)
B \(A\subseteq B\)
C \(A=B^c\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(B\subseteq A\)
Step 1
Concept
Inclusion reverses for complements. Therefore \(A^c\subseteq B^c\) implies \(B\subseteq A\).
Step 2
Why this answer is correct
The correct answer is A. \(B\subseteq A\). Inclusion reverses for complements. Therefore \(A^c\subseteq B^c\) implies \(B\subseteq A\).
Step 3
Exam Tip
पूरकों में समावेशन उलटा होता है। इसलिए \(A^c\subseteq B^c\) से \(B\subseteq A\) मिलेगा।
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यदि (n(U)=80), (n(A)=50), (n(B)=45) और (n\(A\cap B\)=25) है, तो (n(\(A\cup B\)^c)) कितना होगा?
If (n(U)=80), (n(A)=50), (n(B)=45), and (n\(A\cap B\)=25), what is (n(\(A\cup B\)^c))?
#sets
#complement
#cardinality
#two_sets
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A (10)
B (70)
C (20)
D (30)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\)=50+45-25=70). Hence (n(\(A\cup B\)^c)=80-70=10).
Step 2
Why this answer is correct
The correct answer is A. (10). (n\(A\cup B\)=50+45-25=70). Hence (n(\(A\cup B\)^c)=80-70=10).
Step 3
Exam Tip
(n\(A\cup B\)=50+45-25=70) है। इसलिए (n(\(A\cup B\)^c)=80-70=10) होगा।
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यदि (n(U)=100), (n\(A^c\)=40), (n\(B^c\)=55) और (n\(A^c\cap B^c\)=20) है, तो (n\(A\cap B\)) कितना होगा?
If (n(U)=100), (n\(A^c\)=40), (n\(B^c\)=55), and (n\(A^c\cap B^c\)=20), what is (n\(A\cap B\))?
#sets
#complement
#de_morgan
#cardinality
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A (25)
B (75)
C (35)
D (20)
Explanation opens after your attempt
Step 1
Concept
The number in \(A^c\cup B^c\) is (40+55-20=75). By De Morgan, (A^c\cup B^c=\(A\cap B\)^c), so (n\(A\cap B\)=25).
Step 2
Why this answer is correct
The correct answer is A. (25). The number in \(A^c\cup B^c\) is (40+55-20=75). By De Morgan, (A^c\cup B^c=\(A\cap B\)^c), so (n\(A\cap B\)=25).
Step 3
Exam Tip
\(A^c\cup B^c\) की संख्या (40+55-20=75) है। डी मॉर्गन से (A^c\cup B^c=\(A\cap B\)^c), इसलिए (n\(A\cap B\)=25)।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,3,4\}\) और \(B=\{4,5,6\}\) है, तो \(A^c-B^c\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,3,4\}\), and \(B=\{4,5,6\}\), what is \(A^c-B^c\)?
#sets
#complement
#set_difference
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A ({5,6})
B ({1,2,3})
C ({7,8,9})
D ({4})
Explanation opens after your attempt
Correct Answer
A. ({5,6})
Step 1
Concept
\(A^c-B^c=A^c\cap B\). Here \(A^c={5,6,7,8,9}\) and \(B=\{4,5,6\}\), so the answer is ({5,6}).
Step 2
Why this answer is correct
The correct answer is A. ({5,6}). \(A^c-B^c=A^c\cap B\). Here \(A^c={5,6,7,8,9}\) and \(B=\{4,5,6\}\), so the answer is ({5,6}).
Step 3
Exam Tip
\(A^c-B^c=A^c\cap B\) होता है। \(A^c={5,6,7,8,9}\) और \(B=\{4,5,6\}\), इसलिए उत्तर ({5,6}) है।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,3,5,7\}\) और \(B=\{2,3,5,8\}\) है, तो ((A-B)^c) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,3,5,7\}\), and \(B=\{2,3,5,8\}\), what is ((A-B)^c)?
#sets
#complement
#difference_complement
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A ({2,3,4,5,6,8})
B ({1,7})
C ({3,5})
D ({1,2,7,8})
Explanation opens after your attempt
Correct Answer
A. ({2,3,4,5,6,8})
Step 1
Concept
First (A-B={1,7}). Removing it from (U) gives ((A-B)^c={2,3,4,5,6,8}).
Step 2
Why this answer is correct
The correct answer is A. ({2,3,4,5,6,8}). First (A-B={1,7}). Removing it from (U) gives ((A-B)^c={2,3,4,5,6,8}).
Step 3
Exam Tip
पहले (A-B={1,7}) है। (U) से इसे हटाने पर ((A-B)^c={2,3,4,5,6,8}) मिलता है।
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\(यदि (U={x:x\in\mathbb{N},1\le x\le 30}) और (A={x:x\) 2 या 3 से विभाज्य है\(}) है, तो (n(A^c)) कितना होगा\)?
\(If (U={x:x\in\mathbb{N},1\le x\le 30}) and (A={x:x\) is divisible by 2 or \(3}), what is (n(A^c))\)?
#sets
#complement
#counting
#divisibility
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A (10)
B (20)
C (15)
D (5)
Explanation opens after your attempt
Step 1
Concept
Numbers divisible by (2) or (3) are (15+10-5=20). So the complement has (30-20=10) numbers.
Step 2
Why this answer is correct
The correct answer is A. (10). Numbers divisible by (2) or (3) are (15+10-5=20). So the complement has (30-20=10) numbers.
Step 3
Exam Tip
(2) या (3) से विभाज्य संख्याएं (15+10-5=20) हैं। इसलिए पूरक में (30-20=10) संख्याएं होंगी।
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\(यदि (U={x:x\in\mathbb{N},1\le x\le 50}) और (A={x:x\) 5 से विभाज्य है\(}) है, तो (n(A^c)) कितना होगा\)?
\(If (U={x:x\in\mathbb{N},1\le x\le 50}) and (A={x:x\) is divisible by \(5}), what is (n(A^c))\)?
#sets
#complement
#multiples
#cardinality
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A (40)
B (10)
C (45)
D (50)
Explanation opens after your attempt
Step 1
Concept
There are (10) multiples of (5) from (1) to (50). Therefore (n\(A^c\)=50-10=40).
Step 2
Why this answer is correct
The correct answer is A. (40). There are (10) multiples of (5) from (1) to (50). Therefore (n\(A^c\)=50-10=40).
Step 3
Exam Tip
(1) से (50) तक (5) के (10) गुणज हैं। इसलिए (n\(A^c\)=50-10=40) होगा।
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\(यदि (U={1,2,3,4,5,6,7,8,9,10}) और (A={x:x\in U\) और \(x^2-5x+6=0}) है, तो (A^c) क्या होगा\)?
\(If (U={1,2,3,4,5,6,7,8,9,10}) and (A={x:x\in U\) and \(x^2-5x+6=0}), what is (A^c)\)?
#sets
#complement
#quadratic_condition
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A ({1,4,5,6,7,8,9,10})
B ({2,3})
C ({1,2,3,4,5})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,4,5,6,7,8,9,10})
Step 1
Concept
From \(x^2-5x+6=0\), (x=2,3). Removing (2) and (3) from (U) gives the complement.
Step 2
Why this answer is correct
The correct answer is A. ({1,4,5,6,7,8,9,10}). From \(x^2-5x+6=0\), (x=2,3). Removing (2) and (3) from (U) gives the complement.
Step 3
Exam Tip
\(x^2-5x+6=0\) से (x=2,3) मिलते हैं। (U) से (2) और (3) हटाने पर पूरक मिलता है।
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यदि \(U={x:x\in\mathbb{Z},-5\le x\le 5}\) और \(A={x:x^2=9}\) है, तो \(A^c\) में कितने तत्व होंगे?
If \(U={x:x\in\mathbb{Z},-5\le x\le 5}\) and \(A={x:x^2=9}\), how many elements are in \(A^c\)?
#sets
#complement
#integers
#cardinality
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A (9)
B (2)
C (11)
D (7)
Explanation opens after your attempt
Step 1
Concept
There are (11) integers in (U), and \(A=\{-3,3\}\). Hence (n\(A^c\)=11-2=9).
Step 2
Why this answer is correct
The correct answer is A. (9). There are (11) integers in (U), and \(A=\{-3,3\}\). Hence (n\(A^c\)=11-2=9).
Step 3
Exam Tip
(U) में (11) पूर्णांक हैं और \(A=\{-3,3\}\) है। इसलिए (n\(A^c\)=11-2=9) होगा।
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यदि (U) में (120) विद्यार्थी हैं, (72) विद्यार्थी हिंदी पढ़ते हैं और (55) विद्यार्थी अंग्रेजी पढ़ते हैं, जबकि (30) दोनों पढ़ते हैं, तो न हिंदी न अंग्रेजी पढ़ने वाले विद्यार्थी कितने हैं?
If (U) has (120) students, (72) study Hindi and (55) study English, while (30) study both, how many students study neither Hindi nor English?
#sets
#complement
#word_problem
#two_sets
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A (23)
B (97)
C (17)
D (30)
Explanation opens after your attempt
Step 1
Concept
Students studying Hindi or English are (72+55-30=97). Therefore the complement has (120-97=23) students.
Step 2
Why this answer is correct
The correct answer is A. (23). Students studying Hindi or English are (72+55-30=97). Therefore the complement has (120-97=23) students.
Step 3
Exam Tip
हिंदी या अंग्रेजी पढ़ने वाले (72+55-30=97) हैं। इसलिए पूरक में (120-97=23) विद्यार्थी हैं।
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यदि (U) किसी कक्षा के (90) विद्यार्थी हैं और (A) विज्ञान पसंद करने वाले विद्यार्थी हैं। यदि (n\(A^c\)=34), तो विज्ञान पसंद करने वाले विद्यार्थी कितने हैं?
If (U) is the set of (90) students in a class and (A) is the set of students who like science. If (n\(A^c\)=34), how many students like science?
#sets
#complement
#word_problem
#reverse_count
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A (56)
B (124)
C (34)
D (90)
Explanation opens after your attempt
Step 1
Concept
(n(A)=n(U)-n\(A^c\)). So the number who like science is (90-34=56).
Step 2
Why this answer is correct
The correct answer is A. (56). (n(A)=n(U)-n\(A^c\)). So the number who like science is (90-34=56).
Step 3
Exam Tip
(n(A)=n(U)-n\(A^c\)) होता है। इसलिए विज्ञान पसंद करने वाले (90-34=56) हैं।
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\(यदि (U={1,2,3,\ldots,25}) और (A={x:x\) पूर्ण वर्ग है\(}) है, तो (A^c) में कितने तत्व होंगे\)?
\(If (U={1,2,3,\ldots,25}) and (A={x:x\) is a perfect square\(}), how many elements are in (A^c)\)?
#sets
#complement
#perfect_squares
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A (20)
B (5)
C (19)
D (25)
Explanation opens after your attempt
Step 1
Concept
The perfect squares from (1) to (25) are (1,4,9,16,25). Hence (n\(A^c\)=25-5=20).
Step 2
Why this answer is correct
The correct answer is A. (20). The perfect squares from (1) to (25) are (1,4,9,16,25). Hence (n\(A^c\)=25-5=20).
Step 3
Exam Tip
(1) से (25) तक पूर्ण वर्ग (1,4,9,16,25) हैं। इसलिए (n\(A^c\)=25-5=20) होगा।
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\(यदि (U={1,2,3,\ldots,15}) और (A={x:x\) विषम है\(}) है, तो (A^c\cap{x:x\) 3 से विभाज्य है}) क्या होगा?
\(If (U={1,2,3,\ldots,15}) and (A={x:x\) is odd\(}), what is (A^c\cap{x:x\) is divisible by 3})?
#sets
#complement
#intersection
#divisibility
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A ({6,12})
B ({3,6,9,12,15})
C ({2,4,6,8,10,12,14})
D ({3,9,15})
Explanation opens after your attempt
Correct Answer
A. ({6,12})
Step 1
Concept
\(A^c\) contains even numbers. The even numbers divisible by (3) are (6) and (12).
Step 2
Why this answer is correct
The correct answer is A. ({6,12}). \(A^c\) contains even numbers. The even numbers divisible by (3) are (6) and (12).
Step 3
Exam Tip
\(A^c\) में सम संख्याएं हैं। (3) से विभाज्य सम संख्याएं (6) और (12) हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,3,4\}\) और \(A^c\subseteq B\subseteq U\) है, तो (B) के लिए न्यूनतम संभव समुच्चय कौन सा है?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,3,4\}\), and \(A^c\subseteq B\subseteq U\), what is the smallest possible set (B)?
#sets
#complement
#subset
#minimum_set
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A ({5,6,7,8,9})
B ({1,2,3,4})
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({5,6,7,8,9})
Step 1
Concept
The smallest (B) will be exactly \(A^c\). Here \(A^c={5,6,7,8,9}\).
Step 2
Why this answer is correct
The correct answer is A. ({5,6,7,8,9}). The smallest (B) will be exactly \(A^c\). Here \(A^c={5,6,7,8,9}\).
Step 3
Exam Tip
न्यूनतम (B) वही होगा जो \(A^c\) है। यहां \(A^c={5,6,7,8,9}\) है।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(A=\{1,2,3\}\) है, तो ऐसा कौन सा (B) होगा जिससे \(B=A^c\) सत्य हो?
If \(U=\{1,2,3,4,5,6\}\) and \(A=\{1,2,3\}\), which (B) makes \(B=A^c\) true?
#sets
#complement
#identify_set
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A ({4,5,6})
B ({1,2,3})
C ({1,4,5})
D (U)
Explanation opens after your attempt
Correct Answer
A. ({4,5,6})
Step 1
Concept
\(A^c\) contains the elements of (U) that are not in (A). Therefore \(B=\{4,5,6\}\) is needed.
Step 2
Why this answer is correct
The correct answer is A. ({4,5,6}). \(A^c\) contains the elements of (U) that are not in (A). Therefore \(B=\{4,5,6\}\) is needed.
Step 3
Exam Tip
\(A^c\) में (U) के वे तत्व होंगे जो (A) में नहीं हैं। इसलिए \(B=\{4,5,6\}\) चाहिए।
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यदि \(U=\{a,b,c,d,e,f\}\), \(A=\{a,c,e\}\) और \(B=\{b,d,f\}\) है, तो कौन सा कथन सही है?
If \(U=\{a,b,c,d,e,f\}\), \(A=\{a,c,e\}\), and \(B=\{b,d,f\}\), which statement is correct?
#sets
#complement
#verification
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A \(B=A^c\)
B (B=A)
C \(A\cap B=A\)
D \(A\cup B=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(B=A^c\)
Step 1
Concept
(A) and (B) are disjoint and together form (U). Therefore (B) is the complement of (A).
Step 2
Why this answer is correct
The correct answer is A. \(B=A^c\). (A) and (B) are disjoint and together form (U). Therefore (B) is the complement of (A).
Step 3
Exam Tip
(A) और (B) असंबद्ध हैं और दोनों मिलकर (U) बनाते हैं। इसलिए (B), (A) का पूरक है।
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यदि \(A\cap B=\varnothing\) और \(A\cup B=U\) है, तो (B) किसके बराबर होगा?
If \(A\cap B=\varnothing\) and \(A\cup B=U\), then (B) is equal to what?
#sets
#complement
#property_check
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A \(A^c\)
B (A)
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(A^c\)
Step 1
Concept
If two sets are disjoint and together form (U), then they are complements of each other. Hence \(B=A^c\).
Step 2
Why this answer is correct
The correct answer is A. \(A^c\). If two sets are disjoint and together form (U), then they are complements of each other. Hence \(B=A^c\).
Step 3
Exam Tip
यदि दो समुच्चय असंबद्ध हों और मिलकर (U) बनाएं, तो वे एक-दूसरे के पूरक होते हैं। इसलिए \(B=A^c\) होगा।
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यदि \(A\cup A^c=U\) और \(A\cap A^c=\varnothing\), तो (n(A)+n\(A^c\)) किसके बराबर है?
If \(A\cup A^c=U\) and \(A\cap A^c=\varnothing\), then (n(A)+n\(A^c\)) is equal to what?
#sets
#complement
#cardinality_property
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A (n(U))
B (0)
C (2n(U))
D (n\(A\cap A^c\))
Explanation opens after your attempt
Step 1
Concept
(A) and \(A^c\) are disjoint and together form (U). Therefore the sum of their cardinalities is (n(U)).
Step 2
Why this answer is correct
The correct answer is A. (n(U)). (A) and \(A^c\) are disjoint and together form (U). Therefore the sum of their cardinalities is (n(U)).
Step 3
Exam Tip
(A) और \(A^c\) असंबद्ध हैं और मिलकर (U) बनाते हैं। इसलिए उनकी संख्याओं का योग (n(U)) होता है।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4,5\}\) है, तो (\(A^c\)^c\cap{2,4,6,8}) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4,5\}\), what is (\(A^c\)^c\cap{2,4,6,8})?
#sets
#complement
#double_complement
#intersection
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A ({2,4})
B ({6,8})
C ({1,3,5})
D ({2,4,6,8})
Explanation opens after your attempt
Correct Answer
A. ({2,4})
Step 1
Concept
(\(A^c\)^c=A). Therefore \(A\cap{2,4,6,8}={2,4}\).
Step 2
Why this answer is correct
The correct answer is A. ({2,4}). (\(A^c\)^c=A). Therefore \(A\cap{2,4,6,8}={2,4}\).
Step 3
Exam Tip
(\(A^c\)^c=A) होता है। इसलिए \(A\cap{2,4,6,8}={2,4}\) है।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\) और \(A=\{2,5,8\}\) है, तो \(A^c\cup{5}\) में कितने तत्व होंगे?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A=\{2,5,8\}\), how many elements are in \(A^c\cup{5}\)?
#sets
#complement
#cardinality
#union
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A (8)
B (7)
C (10)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(A^c\) has (7) elements because (A) has (3) elements. Since (5) is not in \(A^c\), adding it makes the count (8).
Step 2
Why this answer is correct
The correct answer is A. (8). \(A^c\) has (7) elements because (A) has (3) elements. Since (5) is not in \(A^c\), adding it makes the count (8).
Step 3
Exam Tip
\(A^c\) में (7) तत्व हैं क्योंकि (A) में (3) तत्व हैं। (5) \(A^c\) में नहीं है, इसलिए जोड़ने पर संख्या (8) होगी।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\) और \(A=\{2,4,6\}\) है, तो \(A^c-{1,3,5}\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(A=\{2,4,6\}\), what is \(A^c-{1,3,5}\)?
#sets
#complement
#set_difference
#application
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A ({7,8,9})
B ({1,3,5,7,8,9})
C ({2,4,6})
D ({1,3,5})
Explanation opens after your attempt
Correct Answer
A. ({7,8,9})
Step 1
Concept
\(A^c={1,3,5,7,8,9}\). Removing ({1,3,5}) gives ({7,8,9}).
Step 2
Why this answer is correct
The correct answer is A. ({7,8,9}). \(A^c={1,3,5,7,8,9}\). Removing ({1,3,5}) gives ({7,8,9}).
Step 3
Exam Tip
\(A^c={1,3,5,7,8,9}\) है। इसमें से ({1,3,5}) हटाने पर ({7,8,9}) मिलता है।
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\(यदि (U={x:x\) एक अंक है\(}) और (A={x:x\) सम अंक है\(}), तो (A^c) में कितने तत्व हैं\)?
\(If (U={x:x\) is a digit\(}) and (A={x:x\) is an even digit\(}), how many elements are in (A^c)\)?
#sets
#complement
#digits
#counting
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A (5)
B (4)
C (6)
D (10)
Explanation opens after your attempt
Step 1
Concept
The digit set is \(U=\{0,1,2,3,4,5,6,7,8,9\}\). There are (5) even digits, so there are (5) odd digits.
Step 2
Why this answer is correct
The correct answer is A. (5). The digit set is \(U=\{0,1,2,3,4,5,6,7,8,9\}\). There are (5) even digits, so there are (5) odd digits.
Step 3
Exam Tip
अंकों का \(U=\{0,1,2,3,4,5,6,7,8,9\}\) है। सम अंक (5) हैं, इसलिए विषम अंक भी (5) हैं।
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\(यदि (U={x:x\in\mathbb{N},1\le x\le 12}) और (A={x:x\) 2 और 3 दोनों से विभाज्य है\(}), तो (A^c) क्या होगा\)?
\(If (U={x:x\in\mathbb{N},1\le x\le 12}) and (A={x:x\) is divisible by both 2 and \(3}), what is (A^c)\)?
#sets
#complement
#divisibility
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A ({1,2,3,4,5,7,8,9,10,11})
B ({6,12})
C ({2,3,4,6,8,9,10,12})
D ({1,5,7,11})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4,5,7,8,9,10,11})
Step 1
Concept
Divisible by both means divisible by (6), so \(A=\{6,12\}\). The remaining elements are \(A^c\).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4,5,7,8,9,10,11}). Divisible by both means divisible by (6), so \(A=\{6,12\}\). The remaining elements are \(A^c\).
Step 3
Exam Tip
दोनों से विभाज्य होने का अर्थ (6) से विभाज्य होना है, इसलिए \(A=\{6,12\}\)। बाकी तत्व \(A^c\) हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,3,5,7\}\) और \(C=A^c\) है, तो \(C^c\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,3,5,7\}\), and \(C=A^c\), what is \(C^c\)?
#sets
#complement
#double_complement
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A ({1,3,5,7})
B ({2,4,6,8})
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,7})
Step 1
Concept
\(C=A^c\), so (C^c=\(A^c\)^c=A). The double complement returns the original set.
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,7}). \(C=A^c\), so (C^c=\(A^c\)^c=A). The double complement returns the original set.
Step 3
Exam Tip
\(C=A^c\) है, इसलिए (C^c=\(A^c\)^c=A)। दोहरे पूरक में मूल समुच्चय वापस आता है।
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कथन \(A\cap A^c=\varnothing\) और \(A\cup A^c=U\) से कौन सा निष्कर्ष निकलता है?
From the statements \(A\cap A^c=\varnothing\) and \(A\cup A^c=U\), which conclusion follows?
#sets
#complement
#partition
#concept
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A (A) और \(A^c\) (U) का विभाजन बनाते हैं / (A) and \(A^c\) form a partition of (U)
B \(A=A^c\)
C \(A=\varnothing\) हमेशा / \(A=\varnothing\) always
D (A=U) हमेशा / (A=U) always
Explanation opens after your attempt
Correct Answer
A. (A) और \(A^c\) (U) का विभाजन बनाते हैं / (A) and \(A^c\) form a partition of (U)
Step 1
Concept
Two disjoint sets that together form (U) make a partition of (U). This is the conceptual meaning of complement.
Step 2
Why this answer is correct
The correct answer is A. (A) और \(A^c\) (U) का विभाजन बनाते हैं / (A) and \(A^c\) form a partition of (U). Two disjoint sets that together form (U) make a partition of (U). This is the conceptual meaning of complement.
Step 3
Exam Tip
दो असंबद्ध समुच्चय जो मिलकर (U) बनाते हैं, (U) का विभाजन बनाते हैं। यह पूरक का वैचारिक अर्थ है।
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यदि \(U=\{1,2,3,4,5,6\}\) है और (A) ऐसा समुच्चय है कि \(A=A^c\), तो कौन सा कथन सही है?
If \(U=\{1,2,3,4,5,6\}\) and (A) is a set such that \(A=A^c\), which statement is correct?
#sets
#complement
#reasoning
#impossible
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A ऐसा कोई (A) नहीं हो सकता / no such (A) can exist
B \(A=\{1,2,3\}\)
C \(A=\varnothing\)
D (A=U)
Explanation opens after your attempt
Correct Answer
A. ऐसा कोई (A) नहीं हो सकता / no such (A) can exist
Step 1
Concept
If \(A=A^c\), then \(A\cap A^c=A\), but \(A\cap A^c=\varnothing\). This would force \(A=\varnothing\), but then \(A^c=U\), so it is impossible.
Step 2
Why this answer is correct
The correct answer is A. ऐसा कोई (A) नहीं हो सकता / no such (A) can exist. If \(A=A^c\), then \(A\cap A^c=A\), but \(A\cap A^c=\varnothing\). This would force \(A=\varnothing\), but then \(A^c=U\), so it is impossible.
Step 3
Exam Tip
यदि \(A=A^c\), तो \(A\cap A^c=A\) होगा, लेकिन \(A\cap A^c=\varnothing\) होता है। इससे \(A=\varnothing\) चाहिए, पर तब \(A^c=U\), इसलिए संभव नहीं है।
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यदि (U) बदल जाए लेकिन (A) वही रहे, तो \(A^c\) के बारे में कौन सा कथन सही है?
If (U) changes but (A) remains the same, which statement about \(A^c\) is correct?
#sets
#complement
#universal_set_dependency
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A \(A^c\) बदल सकता है / \(A^c\) may change
B \(A^c\) कभी नहीं बदलता / \(A^c\) never changes
C \(A^c=A\) हो जाता है / \(A^c=A\) becomes true
D \(A^c=\varnothing\) हमेशा / \(A^c=\varnothing\) always
Explanation opens after your attempt
Correct Answer
A. \(A^c\) बदल सकता है / \(A^c\) may change
Step 1
Concept
Complement is always relative to the universal set. Therefore \(A^c\) may change when (U) changes.
Step 2
Why this answer is correct
The correct answer is A. \(A^c\) बदल सकता है / \(A^c\) may change. Complement is always relative to the universal set. Therefore \(A^c\) may change when (U) changes.
Step 3
Exam Tip
पूरक हमेशा सार्वत्रिक समुच्चय के सापेक्ष होता है। इसलिए (U) बदलने पर \(A^c\) भी बदल सकता है।
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यदि \(U_1={1,2,3,4}\), \(U_2={1,2,3,4,5,6}\) और \(A=\{1,2\}\) है, तो \(U_2\) के सापेक्ष \(A^c\) और \(U_1\) के सापेक्ष \(A^c\) में अंतर कौन सा है?
If \(U_1={1,2,3,4}\), \(U_2={1,2,3,4,5,6}\), and \(A=\{1,2\}\), what is the difference between \(A^c\) relative to \(U_2\) and \(A^c\) relative to \(U_1\)?
#sets
#complement
#universal_dependency
#difference
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A ({5,6})
B ({3,4})
C ({1,2})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({5,6})
Step 1
Concept
Relative to \(U_2\), the complement is ({3,4,5,6}), and relative to \(U_1\), it is ({3,4}). The difference is ({5,6}).
Step 2
Why this answer is correct
The correct answer is A. ({5,6}). Relative to \(U_2\), the complement is ({3,4,5,6}), and relative to \(U_1\), it is ({3,4}). The difference is ({5,6}).
Step 3
Exam Tip
\(U_2\) में पूरक ({3,4,5,6}) और \(U_1\) में पूरक ({3,4}) है। अंतर ({5,6}) है।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6\}\) है, तो (\(A^c\cap B\)^c) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4\}\), and \(B=\{3,4,5,6\}\), what is (\(A^c\cap B\)^c)?
#sets
#complement
#nested_operations
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A ({1,2,3,4,7,8,9,10})
B ({5,6})
C ({1,2,7,8,9,10})
D ({3,4,5,6})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4,7,8,9,10})
Step 1
Concept
\(A^c={5,6,7,8,9,10}\) and \(A^c\cap B={5,6}\). Its complement is (U-{5,6}).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4,7,8,9,10}). \(A^c={5,6,7,8,9,10}\) and \(A^c\cap B={5,6}\). Its complement is (U-{5,6}).
Step 3
Exam Tip
\(A^c={5,6,7,8,9,10}\) और \(A^c\cap B={5,6}\) है। इसका पूरक (U-{5,6}) होगा।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{2,4,6,8\}\) और \(B=\{1,2,3,4\}\) है, तो (\(A^c\cup B\)^c) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{2,4,6,8\}\), and \(B=\{1,2,3,4\}\), what is (\(A^c\cup B\)^c)?
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A ({6,8})
B ({1,2,3,4,5,7,9})
C ({5,7,9})
D ({2,4})
Explanation opens after your attempt
Correct Answer
A. ({6,8})
Step 1
Concept
\(A^c={1,3,5,7,9}\), and \(A^c\cup B={1,2,3,4,5,7,9}\). The remaining elements in (U) are (6,8).
Step 2
Why this answer is correct
The correct answer is A. ({6,8}). \(A^c={1,3,5,7,9}\), and \(A^c\cup B={1,2,3,4,5,7,9}\). The remaining elements in (U) are (6,8).
Step 3
Exam Tip
\(A^c={1,3,5,7,9}\) है और \(A^c\cup B={1,2,3,4,5,7,9}\) है। (U) में बचे (6,8) हैं।
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\(यदि (U={x:x\in\mathbb{N},1\le x\le 18}), (A={x:x\) 3 से विभाज्य है\(}) और (B={x:x\) सम है\(}) है, तो (A^c\cap B^c) में कितने तत्व होंगे\)?
\(If (U={x:x\in\mathbb{N},1\le x\le 18}), (A={x:x\) is divisible by \(3}), and (B={x:x\) is even\(}), how many elements are in (A^c\cap B^c)\)?
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#complement
#counting
#de_morgan
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A (6)
B (12)
C (3)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(A^c\cap B^c\) contains numbers that are neither divisible by (3) nor even. These are (1,5,7,11,13,17).
Step 2
Why this answer is correct
The correct answer is A. (6). \(A^c\cap B^c\) contains numbers that are neither divisible by (3) nor even. These are (1,5,7,11,13,17).
Step 3
Exam Tip
\(A^c\cap B^c\) में वे संख्याएं हैं जो न (3) से विभाज्य हैं और न सम हैं। ऐसी संख्याएं (1,5,7,11,13,17) हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10,11,12\}\), \(A=\{1,2,3,4,5,6\}\) और \(B=\{2,4,6,8,10,12\}\) है, तो \(A^c\cup B^c\) में कितने तत्व होंगे?
If \(U=\{1,2,3,4,5,6,7,8,9,10,11,12\}\), \(A=\{1,2,3,4,5,6\}\), and \(B=\{2,4,6,8,10,12\}\), how many elements are in \(A^c\cup B^c\)?
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A (9)
B (3)
C (6)
D (12)
Explanation opens after your attempt
Step 1
Concept
(A^c\cup B^c=\(A\cap B\)^c). Since \(A\cap B={2,4,6}\), the complement has (12-3=9) elements.
Step 2
Why this answer is correct
The correct answer is A. (9). (A^c\cup B^c=\(A\cap B\)^c). Since \(A\cap B={2,4,6}\), the complement has (12-3=9) elements.
Step 3
Exam Tip
(A^c\cup B^c=\(A\cap B\)^c) है। \(A\cap B={2,4,6}\), इसलिए पूरक में (12-3=9) तत्व होंगे।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3\}\) और \(B=\{4,5\}\) है, तो \(A^c\cap B^c\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3\}\), and \(B=\{4,5\}\), what is \(A^c\cap B^c\)?
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#finite
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A ({6,7,8})
B ({1,2,3,4,5})
C ({4,5})
D ({1,2,3})
Explanation opens after your attempt
Correct Answer
A. ({6,7,8})
Step 1
Concept
(A^c\cap B^c=\(A\cup B\)^c). Since \(A\cup B={1,2,3,4,5}\), the remaining elements are (6,7,8).
Step 2
Why this answer is correct
The correct answer is A. ({6,7,8}). (A^c\cap B^c=\(A\cup B\)^c). Since \(A\cup B={1,2,3,4,5}\), the remaining elements are (6,7,8).
Step 3
Exam Tip
(A^c\cap B^c=\(A\cup B\)^c) है। \(A\cup B={1,2,3,4,5}\), इसलिए बचे तत्व (6,7,8) हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\) और \(A^c={1,4,9}\) है, तो (A) में कितने तत्व होंगे?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A^c={1,4,9}\), how many elements are in (A)?
#sets
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#reverse_cardinality
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A (7)
B (3)
C (10)
D (13)
Explanation opens after your attempt
Step 1
Concept
(U) has (10) elements and \(A^c\) has (3) elements. Therefore (n(A)=10-3=7).
Step 2
Why this answer is correct
The correct answer is A. (7). (U) has (10) elements and \(A^c\) has (3) elements. Therefore (n(A)=10-3=7).
Step 3
Exam Tip
(U) में (10) तत्व हैं और \(A^c\) में (3) तत्व हैं। इसलिए (n(A)=10-3=7) होगा।
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यदि (n(U)=64) और (n(A)=3n\(A^c\)) है, तो (n\(A^c\)) कितना होगा?
If (n(U)=64) and (n(A)=3n\(A^c\)), what is (n\(A^c\))?
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#algebra
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A (16)
B (48)
C (21)
D (32)
Explanation opens after your attempt
Step 1
Concept
Let (n\(A^c\)=x), then (n(A)=3x). Thus (3x+x=64), giving (x=16).
Step 2
Why this answer is correct
The correct answer is A. (16). Let (n\(A^c\)=x), then (n(A)=3x). Thus (3x+x=64), giving (x=16).
Step 3
Exam Tip
मान लें (n\(A^c\)=x), तब (n(A)=3x)। इसलिए (3x+x=64) से (x=16) मिलता है।
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यदि (n(U)=54) और (n\(A^c\)=2n(A)) है, तो (n(A)) कितना होगा?
If (n(U)=54) and (n\(A^c\)=2n(A)), what is (n(A))?
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A (18)
B (27)
C (36)
D (12)
Explanation opens after your attempt
Step 1
Concept
Let (n(A)=x), then (n\(A^c\)=2x). Hence (x+2x=54), so (x=18).
Step 2
Why this answer is correct
The correct answer is A. (18). Let (n(A)=x), then (n\(A^c\)=2x). Hence (x+2x=54), so (x=18).
Step 3
Exam Tip
मान लें (n(A)=x), तब (n\(A^c\)=2x)। इसलिए (x+2x=54) से (x=18) है।
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\(यदि (A\subseteq U) और (A^c={x:x\in U\) और \(x\notin A}) है, तो (A\cap A^c) खाली क्यों है\)?
\(If (A\subseteq U) and (A^c={x:x\in U\) and \(x\notin A}), why is (A\cap A^c) empty\)?
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A क्योंकि कोई तत्व एक साथ (A) में और (A) में नहीं हो सकता / because no element can be both in (A) and not in (A)
B क्योंकि (A=U) हमेशा होता है / because (A=U) always
C क्योंकि \(A=\varnothing\) हमेशा होता है / because \(A=\varnothing\) always
D क्योंकि \(A^c\not\subseteq U\) होता है / because \(A^c\not\subseteq U\)
Explanation opens after your attempt
Correct Answer
A. क्योंकि कोई तत्व एक साथ (A) में और (A) में नहीं हो सकता / because no element can be both in (A) and not in (A)
Step 1
Concept
The definition of complement has the condition \(x\notin A\). So the same element cannot also be in (A).
Step 2
Why this answer is correct
The correct answer is A. क्योंकि कोई तत्व एक साथ (A) में और (A) में नहीं हो सकता / because no element can be both in (A) and not in (A). The definition of complement has the condition \(x\notin A\). So the same element cannot also be in (A).
Step 3
Exam Tip
पूरक की परिभाषा में \(x\notin A\) शर्त होती है। इसलिए वही तत्व (A) में भी नहीं हो सकता।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\) और \(A=\{1,2,3\}\) है, तो कौन सा (B) (A) का पूरक नहीं है?
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{1,2,3\}\), which (B) is not the complement of (A)?
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A ({4,5,6,7})
B ({4,5,6,7,8})
C (U-A)
D \(({x:x\in U\) और \(x\notin A})\) / \(({x:x\in U\) and \(x\notin A})\)
Explanation opens after your attempt
Correct Answer
A. ({4,5,6,7})
Step 1
Concept
The correct complement is ({4,5,6,7,8}). The option ({4,5,6,7}) misses (8).
Step 2
Why this answer is correct
The correct answer is A. ({4,5,6,7}). The correct complement is ({4,5,6,7,8}). The option ({4,5,6,7}) misses (8).
Step 3
Exam Tip
सही पूरक ({4,5,6,7,8}) है। विकल्प ({4,5,6,7}) में (8) छूट गया है।
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\(यदि (U={x:x\in\mathbb{N},1\le x\le 100}) और (A={x:x\) 10 से विभाज्य है\(}) है, तो (A^c) में कितने तत्व होंगे\)?
\(If (U={x:x\in\mathbb{N},1\le x\le 100}) and (A={x:x\) is divisible by \(10}), how many elements are in (A^c)\)?
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#multiples
#counting
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A (90)
B (10)
C (100)
D (80)
Explanation opens after your attempt
Step 1
Concept
There are (10) multiples of (10) from (1) to (100). Therefore the complement has (100-10=90) elements.
Step 2
Why this answer is correct
The correct answer is A. (90). There are (10) multiples of (10) from (1) to (100). Therefore the complement has (100-10=90) elements.
Step 3
Exam Tip
(1) से (100) तक (10) के (10) गुणज हैं। इसलिए पूरक में (100-10=90) तत्व होंगे।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,3,5,7,9\}\) और \(B=A^c\) है, तो \(A\cup B\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,3,5,7,9\}\), and \(B=A^c\), what is \(A\cup B\)?
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#union_property
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A (U)
B \(\varnothing\)
C (A)
D (B)
Explanation opens after your attempt
Step 1
Concept
If \(B=A^c\), then \(A\cup B=A\cup A^c=U\). This is a direct property of complement.
Step 2
Why this answer is correct
The correct answer is A. (U). If \(B=A^c\), then \(A\cup B=A\cup A^c=U\). This is a direct property of complement.
Step 3
Exam Tip
यदि \(B=A^c\), तो \(A\cup B=A\cup A^c=U\) होगा। यह पूरक का सीधा गुण है।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{2,4,6,8,10\}\) और \(B=A^c\) है, तो \(A\cap B\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{2,4,6,8,10\}\), and \(B=A^c\), what is \(A\cap B\)?
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A \(\varnothing\)
B (U)
C (A)
D (B)
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Correct Answer
A. \(\varnothing\)
Step 1
Concept
If \(B=A^c\), then \(A\cap B=A\cap A^c=\varnothing\). Complementary sets are always disjoint.
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). If \(B=A^c\), then \(A\cap B=A\cap A^c=\varnothing\). Complementary sets are always disjoint.
Step 3
Exam Tip
यदि \(B=A^c\), तो \(A\cap B=A\cap A^c=\varnothing\) होगा। पूरक समुच्चय हमेशा असंबद्ध होते हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4\}\) और \(B=\{5,6,7,8\}\) है, तो (\(A\cup B\)^c) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4\}\), and \(B=\{5,6,7,8\}\), what is (\(A\cup B\)^c)?
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A \(\varnothing\)
B (U)
C (A)
D (B)
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Correct Answer
A. \(\varnothing\)
Step 1
Concept
Here \(A\cup B=U\). Therefore (\(A\cup B\)^c=U^c=\varnothing).
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). Here \(A\cup B=U\). Therefore (\(A\cup B\)^c=U^c=\varnothing).
Step 3
Exam Tip
यहां \(A\cup B=U\) है। इसलिए (\(A\cup B\)^c=U^c=\varnothing) होगा।
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यदि \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\) और \(B=\{4,5,6\}\) है, तो (\(A\cap B\)^c) क्या होगा?
If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), and \(B=\{4,5,6\}\), what is (\(A\cap B\)^c)?
#sets
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#intersection_complement
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A (U)
B \(\varnothing\)
C (A)
D (B)
Explanation opens after your attempt
Step 1
Concept
Here \(A\cap B=\varnothing\). Therefore (\(A\cap B\)^c=\varnothing^c=U).
Step 2
Why this answer is correct
The correct answer is A. (U). Here \(A\cap B=\varnothing\). Therefore (\(A\cap B\)^c=\varnothing^c=U).
Step 3
Exam Tip
यहां \(A\cap B=\varnothing\) है। इसलिए (\(A\cap B\)^c=\varnothing^c=U) होगा।
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