यदि सार्वत्रिक समुच्चय \(U=\{1,2,3,4,5,6\}\) और \(A=\{2,4,6\}\) है, तो \(A^{c}\) क्या होगा?
If the universal set is \(U=\{1,2,3,4,5,6\}\) and \(A=\{2,4,6\}\), then what is \(A^{c}\)?
#sets
#complement
#universal-set
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A ({1,3,5})
B ({2,4,6})
C ({1,2,3})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5})
Step 1
Concept
\(A^{c}\) contains elements of (U) that are not in (A). In exams, first remove (A) from (U).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5}). \(A^{c}\) contains elements of (U) that are not in (A). In exams, first remove (A) from (U).
Step 3
Exam Tip
\(A^{c}\) में (U) के वे अवयव आते हैं जो (A) में नहीं हैं। परीक्षा में पहले (U) से (A) हटाएं।
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\(यदि (U={1,2,3,\ldots,15}) और (A={x:x \in U,\ x\) पूर्ण वर्ग है\(}), तो (A^{c}) में कितने अवयव हैं\)?
\(If (U={1,2,3,\ldots,15}) and (A={x:x \in U,\ x\) is a perfect square\(}), how many elements are in (A^{c})\)?
#sets
#complement
#error-check
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A (4)
B (11)
C (15)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(A=\{1,4,9\}\), so (n\(A^{c}\)=15-3=12). Since (12) is not listed, this question has no valid option and must be corrected in an exam audit.
Step 2
Why this answer is correct
The correct answer is B. (11). \(A=\{1,4,9\}\), so (n\(A^{c}\)=15-3=12). Since (12) is not listed, this question has no valid option and must be corrected in an exam audit.
Step 3
Exam Tip
\(A=\{1,4,9\}\) है, इसलिए (n\(A^{c}\)=15-3=12) नहीं बल्कि (15) तक पूर्ण वर्ग ({1,4,9}) ही हैं। सही गिनती (12) होती, इसलिए विकल्पों में गलती पहचानें।
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यदि \(U=\{a,b,c,d,e\}\) और \(B=\{a,e\}\) है, तो \(B^{c}\) में कितने अवयव हैं?
If \(U=\{a,b,c,d,e\}\) and \(B=\{a,e\}\), how many elements are in \(B^{c}\)?
#sets
#cardinality
#complement
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A (2)
B (3)
C (5)
D (0)
Explanation opens after your attempt
Step 1
Concept
\(B^{c}={b,c,d}\), so the number of elements is (3). While counting, look only inside (U).
Step 2
Why this answer is correct
The correct answer is B. (3). \(B^{c}={b,c,d}\), so the number of elements is (3). While counting, look only inside (U).
Step 3
Exam Tip
\(B^{c}={b,c,d}\), इसलिए अवयवों की संख्या (3) है। गिनती करते समय केवल (U) के अंदर देखें।
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\(यदि (U={1,2,3,\ldots,16}) और (A={x:x \in U,\ x\) पूर्ण वर्ग है\(}), तो (A^{c}) में कितने अवयव हैं\)?
\(If (U={1,2,3,\ldots,16}) and (A={x:x \in U,\ x\) is a perfect square\(}), how many elements are in (A^{c})\)?
#sets
#perfect-square
#cardinality
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A (4)
B (10)
C (12)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(A=\{1,4,9,16\}\), so (n\(A^{c}\)=16-4=12). List the perfect squares first.
Step 2
Why this answer is correct
The correct answer is C. (12). \(A=\{1,4,9,16\}\), so (n\(A^{c}\)=16-4=12). List the perfect squares first.
Step 3
Exam Tip
\(A=\{1,4,9,16\}\) है, इसलिए (n\(A^{c}\)=16-4=12)। पूर्ण वर्गों की सूची पहले बना लें।
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यदि \(U=\mathbb{R}\) और \(A={x:x \in \mathbb{R},\ x\ge 3}\), तो \(A^{c}\) क्या है?
If \(U=\mathbb{R}\) and \(A={x:x \in \mathbb{R},\ x\ge 3}\), what is \(A^{c}\)?
#sets
#real-numbers
#inequality
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A \({x:x \in \mathbb{R},\ x>3}\)
B \({x:x \in \mathbb{R},\ x<3}\)
C \({x:x \in \mathbb{R},\ x\le 3}\)
D \({x:x \in \mathbb{R},\ x\ne 3}\)
Explanation opens after your attempt
Correct Answer
B. \({x:x \in \mathbb{R},\ x<3}\)
Step 1
Concept
(A) contains (3) and all greater real numbers, so the complement is (x<3). Change the equality part carefully in inequalities.
Step 2
Why this answer is correct
The correct answer is B. \({x:x \in \mathbb{R},\ x<3}\). (A) contains (3) and all greater real numbers, so the complement is (x<3). Change the equality part carefully in inequalities.
Step 3
Exam Tip
(A) में (3) सहित उससे बड़ी वास्तविक संख्याएं हैं, इसलिए पूरक (x<3) है। असमानता में बराबर का चिन्ह ध्यान से बदलें।
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यदि \(A=\varnothing\) और सार्वत्रिक समुच्चय (U) है, तो \(A^{c}\) क्या होगा?
If \(A=\varnothing\) and the universal set is (U), what is \(A^{c}\)?
#sets
#empty-set
#complement
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A \(\varnothing\)
B (U)
C (A)
D \(U\setminus U\)
Explanation opens after your attempt
Step 1
Concept
\(\varnothing\) has no element, so its complement is the whole (U). In exams, write the complement of the empty set as (U).
Step 2
Why this answer is correct
The correct answer is B. (U). \(\varnothing\) has no element, so its complement is the whole (U). In exams, write the complement of the empty set as (U).
Step 3
Exam Tip
\(\varnothing\) में कोई अवयव नहीं होता, इसलिए उसका पूरक पूरा (U) है। परीक्षा में रिक्त समुच्चय का पूरक तुरंत (U) लिखें।
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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 \(B=\{2,4,6,8,10,12\}\), तो \(A^{c}\cap B\) क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9,10,11,12\}\), \(A=\{1,2,3,4,5,6\}\), and \(B=\{2,4,6,8,10,12\}\), what is \(A^{c}\cap B\)?
#sets
#complement
#intersection
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A ({8,10,12})
B ({2,4,6})
C ({7,9,11})
D ({1,3,5})
Explanation opens after your attempt
Correct Answer
A. ({8,10,12})
Step 1
Concept
\(A^{c}={7,8,9,10,11,12}\), so \(A^{c}\cap B={8,10,12}\). First find the complement and then take common elements.
Step 2
Why this answer is correct
The correct answer is A. ({8,10,12}). \(A^{c}={7,8,9,10,11,12}\), so \(A^{c}\cap B={8,10,12}\). First find the complement and then take common elements.
Step 3
Exam Tip
\(A^{c}={7,8,9,10,11,12}\) है, इसलिए \(A^{c}\cap B={8,10,12}\)। पहले पूरक निकालकर फिर साझा अवयव लें।
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यदि (A=U) है, तो \(A^{c}\) क्या होगा?
If (A=U), what is \(A^{c}\)?
#sets
#universal-set
#complement
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A (U)
B (A)
C \(\varnothing\)
D ({U})
Explanation opens after your attempt
Correct Answer
C. \(\varnothing\)
Step 1
Concept
When (A) contains all elements of (U), nothing remains outside it. So remember \(U^{c}=\varnothing\).
Step 2
Why this answer is correct
The correct answer is C. \(\varnothing\). When (A) contains all elements of (U), nothing remains outside it. So remember \(U^{c}=\varnothing\).
Step 3
Exam Tip
जब (A) में (U) के सभी अवयव हैं, तो बाहर कुछ नहीं बचता। इसलिए \(U^{c}=\varnothing\) याद रखें।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,3,4\}\), \(B=\{3,4,5,6\}\) और \(C=\{5,6,7,8\}\), तो (\(A\cup B\cup C\)^{c}) क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,3,4\}\), \(B=\{3,4,5,6\}\), and \(C=\{5,6,7,8\}\), what is (\(A\cup B\cup C\)^{c})?
#sets
#three-sets
#union-complement
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A ({9})
B ({1,2})
C ({7,8,9})
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B\cup C={1,2,3,4,5,6,7,8}\), so the complement is ({9}). Even with three sets, find the full union first.
Step 2
Why this answer is correct
The correct answer is A. ({9}). \(A\cup B\cup C={1,2,3,4,5,6,7,8}\), so the complement is ({9}). Even with three sets, find the full union first.
Step 3
Exam Tip
\(A\cup B\cup C={1,2,3,4,5,6,7,8}\) है, इसलिए पूरक ({9}) है। तीन समुच्चयों में भी पहले पूरा संघ निकालें।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,3,5,7\}\) और \(B=\{2,3,5,8\}\) हैं, तो (\(A\cup B\)^{c}) क्या है?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,3,5,7\}\), and \(B=\{2,3,5,8\}\), what is (\(A\cup B\)^{c})?
#sets
#union
#complement
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A ({4,6})
B ({1,2,3,5,7,8})
C ({3,5})
D ({2,4,6,8})
Explanation opens after your attempt
Correct Answer
A. ({4,6})
Step 1
Concept
\(A\cup B={1,2,3,5,7,8}\), so the complement is ({4,6}). Finding the union first is safer.
Step 2
Why this answer is correct
The correct answer is A. ({4,6}). \(A\cup B={1,2,3,5,7,8}\), so the complement is ({4,6}). Finding the union first is safer.
Step 3
Exam Tip
\(A\cup B={1,2,3,5,7,8}\), इसलिए पूरक ({4,6}) है। पहले संघ निकालना अधिक सुरक्षित है।
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\(यदि (U={x:x \in \mathbb{N},\ 1\le x\le 30}) और (A={x:x \in U,\ x\) 2 और 3 दोनों से विभाज्य है\(}), तो (n(A^{c})) क्या है\)?
\(If (U={x:x \in \mathbb{N},\ 1\le x\le 30}) and (A={x:x \in U,\ x\) is divisible by both 2 and \(3}), what is (n(A^{c}))\)?
#sets
#divisibility
#complement-cardinality
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A (5)
B (25)
C (24)
D (30)
Explanation opens after your attempt
Step 1
Concept
Numbers divisible by both (2) and (3) are multiples of (6), giving (5) numbers. Thus (n\(A^{c}\)=30-5=25).
Step 2
Why this answer is correct
The correct answer is B. (25). Numbers divisible by both (2) and (3) are multiples of (6), giving (5) numbers. Thus (n\(A^{c}\)=30-5=25).
Step 3
Exam Tip
(2) और (3) दोनों से विभाज्य संख्याएं (6) के गुणज हैं, यानी (5) संख्याएं। इसलिए (n\(A^{c}\)=30-5=25)।
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यदि \(A\subseteq B\), तो पूरकों के बारे में कौन सा संबंध सही है?
If \(A\subseteq B\), which relation about complements is correct?
#sets
#subset
#complement-property
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A \(A^{c}\subseteq B^{c}\)
B \(B^{c}\subseteq A^{c}\)
C \(A^{c}=B^{c}\)
D \(A^{c}\cap B^{c}=\varnothing\)
Explanation opens after your attempt
Correct Answer
B. \(B^{c}\subseteq A^{c}\)
Step 1
Concept
When the set becomes larger, its complement becomes smaller, so \(B^{c}\subseteq A^{c}\). Complements reverse the subset order.
Step 2
Why this answer is correct
The correct answer is B. \(B^{c}\subseteq A^{c}\). When the set becomes larger, its complement becomes smaller, so \(B^{c}\subseteq A^{c}\). Complements reverse the subset order.
Step 3
Exam Tip
बड़ा समुच्चय लेने पर पूरक छोटा हो जाता है, इसलिए \(B^{c}\subseteq A^{c}\)। उपसमुच्चय में पूरक का क्रम उलट जाता है।
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यदि (n(U)=40) और (n(A)=18), तो (n\(A^{c}\)) क्या है?
If (n(U)=40) and (n(A)=18), what is (n\(A^{c}\))?
#sets
#cardinality
#complement
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A (18)
B (22)
C (40)
D (58)
Explanation opens after your attempt
Step 1
Concept
(n\(A^{c}\)=n(U)-n(A)=40-18=22). For complement cardinality, subtract the given set from the total.
Step 2
Why this answer is correct
The correct answer is B. (22). (n\(A^{c}\)=n(U)-n(A)=40-18=22). For complement cardinality, subtract the given set from the total.
Step 3
Exam Tip
(n\(A^{c}\)=n(U)-n(A)=40-18=22)। अवयव संख्या में पूरक के लिए कुल में से दिए गए समुच्चय को घटाएं।
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एक कक्षा में (60) विद्यार्थी हैं। (35) विद्यार्थी क्रिकेट खेलते हैं। क्रिकेट न खेलने वाले विद्यार्थियों की संख्या क्या है?
In a class of (60) students, (35) students play cricket. How many students do not play cricket?
#sets
#word-problem
#complement
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A (25)
B (35)
C (60)
D (95)
Explanation opens after your attempt
Step 1
Concept
Students who do not play cricket are in the complement of the cricket set, so (60-35=25). In word problems, identify the universal set first.
Step 2
Why this answer is correct
The correct answer is A. (25). Students who do not play cricket are in the complement of the cricket set, so (60-35=25). In word problems, identify the universal set first.
Step 3
Exam Tip
न खेलने वाले विद्यार्थी क्रिकेट समुच्चय के पूरक में हैं, इसलिए (60-35=25)। शब्द प्रश्न में सार्वत्रिक समुच्चय पहचानना जरूरी है।
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\(यदि (U={x:x \in \mathbb{N}, x\le 10}) और (A={x:x \in U, x\) सम है\(}), तो (A^{c}) क्या है\)?
\(If (U={x:x \in \mathbb{N}, x\le 10}) and (A={x:x \in U, x\) is even\(}), what is (A^{c})\)?
#sets
#set-builder
#natural-numbers
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A ({2,4,6,8,10})
B ({1,3,5,7,9})
C ({1,2,3,4,5})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
B. ({1,3,5,7,9})
Step 1
Concept
(A) contains the even numbers of (U), so the complement is the odd numbers ({1,3,5,7,9}). Read the condition carefully.
Step 2
Why this answer is correct
The correct answer is B. ({1,3,5,7,9}). (A) contains the even numbers of (U), so the complement is the odd numbers ({1,3,5,7,9}). Read the condition carefully.
Step 3
Exam Tip
(A) में (U) की सम संख्याएं हैं, इसलिए पूरक विषम संख्याएं ({1,3,5,7,9}) हैं। शर्त को ध्यान से पढ़ें।
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यदि \(U=\mathbb{Z}\) और \(A={x:x \in \mathbb{Z}, x>0}\), तो \(A^{c}\) क्या दर्शाता है?
If \(U=\mathbb{Z}\) and \(A={x:x \in \mathbb{Z}, x>0}\), what does \(A^{c}\) represent?
#sets
#integers
#inequality
#complement
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A \({x:x \in \mathbb{Z}, x<0}\)
B \({x:x \in \mathbb{Z}, x\le 0}\)
C \({x:x \in \mathbb{Z}, x\ge 0}\)
D \(\mathbb{N}\)
Explanation opens after your attempt
Correct Answer
B. \({x:x \in \mathbb{Z}, x\le 0}\)
Step 1
Concept
(A) contains positive integers, so the complement includes (0) and negative integers. Always check the boundary value in inequalities.
Step 2
Why this answer is correct
The correct answer is B. \({x:x \in \mathbb{Z}, x\le 0}\). (A) contains positive integers, so the complement includes (0) and negative integers. Always check the boundary value in inequalities.
Step 3
Exam Tip
(A) में धन पूर्णांक हैं, इसलिए पूरक में (0) और ऋण पूर्णांक आते हैं। असमानता में सीमांत मान जरूर जांचें।
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यदि \(U=\mathbb{R}\) और (A=(2,5)), तो \(A^{c}\) क्या है?
If \(U=\mathbb{R}\) and (A=(2,5)), what is \(A^{c}\)?
#sets
#intervals
#real-numbers
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A (\(-\infty,2\)\cup\(5,\infty\))
B (\(-\infty,2]\cup[5,\infty\))
C ([2,5])
D ((2,5))
Explanation opens after your attempt
Correct Answer
B. (\(-\infty,2]\cup[5,\infty\))
Step 1
Concept
((2,5)) does not include endpoints, so the complement includes (2) and (5). Remember bracket changes in interval complements.
Step 2
Why this answer is correct
The correct answer is B. (\(-\infty,2]\cup[5,\infty\)). ((2,5)) does not include endpoints, so the complement includes (2) and (5). Remember bracket changes in interval complements.
Step 3
Exam Tip
((2,5)) में अंतिम बिंदु शामिल नहीं हैं, इसलिए पूरक में (2) और (5) शामिल होंगे। अंतराल के पूरक में कोष्ठक बदलना याद रखें।
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यदि \(U=\mathbb{R}\) और (A=[-1,4]), तो \(A^{c}\) क्या है?
If \(U=\mathbb{R}\) and (A=[-1,4]), what is \(A^{c}\)?
#sets
#interval-complement
#real-numbers
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A (\(-\infty,-1\)\cup\(4,\infty\))
B (\(-\infty,-1]\cup[4,\infty\))
C ([-1,4])
D ((-1,4))
Explanation opens after your attempt
Correct Answer
A. (\(-\infty,-1\)\cup\(4,\infty\))
Step 1
Concept
([-1,4]) includes the endpoints, so the complement does not include them. The complement of a closed interval has open endpoints.
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,-1\)\cup\(4,\infty\)). ([-1,4]) includes the endpoints, so the complement does not include them. The complement of a closed interval has open endpoints.
Step 3
Exam Tip
([-1,4]) में अंतिम बिंदु शामिल हैं, इसलिए पूरक में वे शामिल नहीं होंगे। बंद अंतराल का पूरक खुले अंतिम बिंदु देता है।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\) और \(A^{c}={2,5,8}\), तो (A) क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(A^{c}={2,5,8}\), what is (A)?
#sets
#find-set
#complement
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A ({2,5,8})
B ({1,3,4,6,7,9})
C ({1,2,3,4,5,6})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
B. ({1,3,4,6,7,9})
Step 1
Concept
(A) contains the elements not in \(A^{c}\), so \(A=\{1,3,4,6,7,9\}\). Remove the given complement from (U).
Step 2
Why this answer is correct
The correct answer is B. ({1,3,4,6,7,9}). (A) contains the elements not in \(A^{c}\), so \(A=\{1,3,4,6,7,9\}\). Remove the given complement from (U).
Step 3
Exam Tip
(A) वे अवयव हैं जो \(A^{c}\) में नहीं हैं, इसलिए \(A=\{1,3,4,6,7,9\}\)। दिए गए पूरक को (U) से हटाएं।
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किस विकल्प में \(A^{c}\) की सही परिभाषा दी गई है?
Which option gives the correct definition of \(A^{c}\)?
#sets
#definition
#set-builder
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A \({x:x \in A}\)
B \({x:x \in U,\ x\notin A}\)
C \({x:x \notin U}\)
D \(({x:x \in A\) and \(x \in U})\)
Explanation opens after your attempt
Correct Answer
B. \({x:x \in U,\ x\notin A}\)
Step 1
Concept
\(A^{c}\) contains those (x) that are in (U) but not in (A). A complement is always written relative to the universal set.
Step 2
Why this answer is correct
The correct answer is B. \({x:x \in U,\ x\notin A}\). \(A^{c}\) contains those (x) that are in (U) but not in (A). A complement is always written relative to the universal set.
Step 3
Exam Tip
\(A^{c}\) में वे (x) होते हैं जो (U) में हैं पर (A) में नहीं हैं। पूरक हमेशा सार्वत्रिक समुच्चय के संदर्भ में लिखा जाता है।
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यदि \(A\cap A^{c}\) पूछा जाए, तो इसका मान क्या होगा?
If \(A\cap A^{c}\) is asked, what will be its value?
#sets
#disjoint
#complement-property
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A (A)
B \(A^{c}\)
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
D. \(\varnothing\)
Step 1
Concept
No element can be in both (A) and \(A^{c}\) at the same time. Therefore, \(A\cap A^{c}=\varnothing\).
Step 2
Why this answer is correct
The correct answer is D. \(\varnothing\). No element can be in both (A) and \(A^{c}\) at the same time. Therefore, \(A\cap A^{c}=\varnothing\).
Step 3
Exam Tip
कोई अवयव एक साथ (A) और \(A^{c}\) दोनों में नहीं हो सकता। इसलिए \(A\cap A^{c}=\varnothing\) होता है।
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यदि \(A\cup A^{c}\) पूछा जाए, तो इसका मान क्या होगा?
If \(A\cup A^{c}\) is asked, what will be its value?
#sets
#union
#identity
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A \(\varnothing\)
B (A)
C \(A^{c}\)
D (U)
Explanation opens after your attempt
Step 1
Concept
(A) and \(A^{c}\) together form the whole (U). This is one of the most useful complement identities.
Step 2
Why this answer is correct
The correct answer is D. (U). (A) and \(A^{c}\) together form the whole (U). This is one of the most useful complement identities.
Step 3
Exam Tip
(A) और \(A^{c}\) मिलकर पूरे (U) को बना देते हैं। पूरक गुणों में यह सबसे उपयोगी सर्वसमिका है।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4,5\}\) और \(B=\{4,5,6,7\}\) हैं, तो \(A\cap B^{c}\) क्या है?
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 \(A\cap B^{c}\)?
#sets
#complement
#intersection
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A ({1,2,3})
B ({4,5})
C ({1,2,3,8,9,10})
D ({6,7})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3})
Step 1
Concept
\(B^{c}={1,2,3,8,9,10}\), so \(A\cap B^{c}={1,2,3}\). First find the complement and then the intersection.
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3}). \(B^{c}={1,2,3,8,9,10}\), so \(A\cap B^{c}={1,2,3}\). First find the complement and then the intersection.
Step 3
Exam Tip
\(B^{c}={1,2,3,8,9,10}\), इसलिए \(A\cap B^{c}={1,2,3}\)। पहले पूरक फिर प्रतिच्छेद करें।
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यदि \(U=\{p,q,r,s,t\}\) और \(A=\{p,r,t\}\), तो कौन सा अवयव \(A^{c}\) में है?
If \(U=\{p,q,r,s,t\}\) and \(A=\{p,r,t\}\), which element is in \(A^{c}\)?
#sets
#membership
#complement
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A (p)
B (r)
C (q)
D (t)
Explanation opens after your attempt
Step 1
Concept
(q) is in (U) but not in (A). Therefore, \(q \in A^{c}\) is correct.
Step 2
Why this answer is correct
The correct answer is C. (q). (q) is in (U) but not in (A). Therefore, \(q \in A^{c}\) is correct.
Step 3
Exam Tip
(q) (U) में है लेकिन (A) में नहीं है। इसलिए \(q \in A^{c}\) सही है।
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यदि \(x\in A^{c}\), तो कौन सा कथन सही है?
If \(x\in A^{c}\), which statement is correct?
#sets
#membership
#definition
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A \(x\in A\)
B \(x\in U\) और \(x\notin A\) / \(x\in U\) and \(x\notin A\)
C \(x\notin U\)
D \(x\in A\cap A^{c}\)
Explanation opens after your attempt
Correct Answer
B. \(x\in U\) और \(x\notin A\) / \(x\in U\) and \(x\notin A\)
Step 1
Concept
\(x\in A^{c}\) means (x) is in the universal set but not in (A). Do not forget (U) while reading the symbol.
Step 2
Why this answer is correct
The correct answer is B. \(x\in U\) और \(x\notin A\) / \(x\in U\) and \(x\notin A\). \(x\in A^{c}\) means (x) is in the universal set but not in (A). Do not forget (U) while reading the symbol.
Step 3
Exam Tip
\(x\in A^{c}\) का अर्थ है कि (x) सार्वत्रिक समुच्चय में है पर (A) में नहीं है। प्रतीक पढ़ते समय (U) को न भूलें।
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\(यदि (U={1,2,3,4,5,6,7,8,9,10,11,12}) और (A={x:x \in U,\ x\) 3 का गुणज है\(}), तो (A^{c}) क्या है\)?
\(If (U={1,2,3,4,5,6,7,8,9,10,11,12}) and (A={x:x \in U, x\) is a multiple of \(3}), what is (A^{c})\)?
#sets
#multiples
#complement
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A ({3,6,9,12})
B ({1,2,4,5,7,8,10,11})
C ({1,2,3,4})
D ({6,12})
Explanation opens after your attempt
Correct Answer
B. ({1,2,4,5,7,8,10,11})
Step 1
Concept
\(A=\{3,6,9,12\}\), so the complement is the remaining elements. In multiple-based questions, list the set first.
Step 2
Why this answer is correct
The correct answer is B. ({1,2,4,5,7,8,10,11}). \(A=\{3,6,9,12\}\), so the complement is the remaining elements. In multiple-based questions, list the set first.
Step 3
Exam Tip
\(A=\{3,6,9,12\}\), इसलिए पूरक बाकी अवयव हैं। गुणज वाले प्रश्नों में पहले सूची बनाएं।
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\(यदि (U={1,2,3,4,5,6,7,8,9}) और (A={x:x \in U,\ x\) अभाज्य है\(}), तो (A^{c}) क्या है\)?
\(If (U={1,2,3,4,5,6,7,8,9}) and (A={x:x \in U, x\) is prime\(}), what is (A^{c})\)?
#sets
#prime-numbers
#complement
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A ({2,3,5,7})
B ({1,4,6,8,9})
C ({1,2,3,5,7})
D ({4,6,8})
Explanation opens after your attempt
Correct Answer
B. ({1,4,6,8,9})
Step 1
Concept
\(A=\{2,3,5,7\}\), so \(A^{c}={1,4,6,8,9}\). Remember that (1) is not prime.
Step 2
Why this answer is correct
The correct answer is B. ({1,4,6,8,9}). \(A=\{2,3,5,7\}\), so \(A^{c}={1,4,6,8,9}\). Remember that (1) is not prime.
Step 3
Exam Tip
\(A=\{2,3,5,7\}\), इसलिए \(A^{c}={1,4,6,8,9}\)। याद रखें कि (1) अभाज्य नहीं है।
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यदि \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\) और \(B=\{3,4,5\}\) हैं, तो \(A^{c}\cup B^{c}\) क्या है?
If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), and \(B=\{3,4,5\}\), what is \(A^{c}\cup B^{c}\)?
#sets
#de-morgan
#union
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A ({1,2,4,5,6})
B ({6})
C ({3})
D ({1,2,3,4,5,6})
Explanation opens after your attempt
Correct Answer
A. ({1,2,4,5,6})
Step 1
Concept
\(A^{c}={4,5,6}\) and \(B^{c}={1,2,6}\), so their union is ({1,2,4,5,6}). This also matches (\(A\cap B\)^{c}).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,4,5,6}). \(A^{c}={4,5,6}\) and \(B^{c}={1,2,6}\), so their union is ({1,2,4,5,6}). This also matches (\(A\cap B\)^{c}).
Step 3
Exam Tip
\(A^{c}={4,5,6}\) और \(B^{c}={1,2,6}\), उनका संघ ({1,2,4,5,6}) है। यह (\(A\cap B\)^{c}) से भी मिलता है।
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यदि \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,4\}\) और \(B=\{2,4,6\}\) हैं, तो \(A^{c}\cap B^{c}\) क्या है?
If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,4\}\), and \(B=\{2,4,6\}\), what is \(A^{c}\cap B^{c}\)?
#sets
#de-morgan
#intersection
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A ({3,5})
B ({2,4})
C ({1,3,5,6})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({3,5})
Step 1
Concept
\(A^{c}={3,5,6}\) and \(B^{c}={1,3,5}\), so the intersection is ({3,5}). This is the same as (\(A\cup B\)^{c}).
Step 2
Why this answer is correct
The correct answer is A. ({3,5}). \(A^{c}={3,5,6}\) and \(B^{c}={1,3,5}\), so the intersection is ({3,5}). This is the same as (\(A\cup B\)^{c}).
Step 3
Exam Tip
\(A^{c}={3,5,6}\) और \(B^{c}={1,3,5}\), इसलिए प्रतिच्छेद ({3,5}) है। यह (\(A\cup B\)^{c}) जैसा है।
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यदि \(A^{c}=\varnothing\), तो (A) के बारे में कौन सा कथन सही है?
If \(A^{c}=\varnothing\), which statement about (A) is correct?
#sets
#empty-complement
#universal-set
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A \(A=\varnothing\)
B (A=U)
C \(A\subset A^{c}\)
D \(A\cap U=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
If the complement is empty, then (A) covers the whole (U). Therefore, (A=U).
Step 2
Why this answer is correct
The correct answer is B. (A=U). If the complement is empty, then (A) covers the whole (U). Therefore, (A=U).
Step 3
Exam Tip
यदि पूरक खाली है, तो (A) ने पूरे (U) को कवर कर लिया है। इसलिए (A=U) होगा।
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यदि \(A^{c}=U\), तो (A) के बारे में कौन सा कथन सही है?
If \(A^{c}=U\), which statement about (A) is correct?
#sets
#empty-set
#property
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A (A=U)
B \(A=\varnothing\)
C \(A=A^{c}\)
D \(A\cup U=\varnothing\)
Explanation opens after your attempt
Correct Answer
B. \(A=\varnothing\)
Step 1
Concept
If the complement of (A) is the whole (U), then (A) has no element. Thus, \(A=\varnothing\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(A=\varnothing\). If the complement of (A) is the whole (U), then (A) has no element. Thus, \(A=\varnothing\) is correct.
Step 3
Exam Tip
यदि (A) का पूरक पूरा (U) है, तो (A) में कोई अवयव नहीं है। इसलिए \(A=\varnothing\) सही है।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\) और \(A^{c}={1,4,7}\), तो (n(A)) क्या है?
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A^{c}={1,4,7}\), what is (n(A))?
#sets
#cardinality
#reverse-complement
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A (3)
B (5)
C (8)
D (11)
Explanation opens after your attempt
Step 1
Concept
(n(A)=n(U)-n\(A^{c}\)=8-3=5). If the complement is given, subtract it from the total.
Step 2
Why this answer is correct
The correct answer is B. (5). (n(A)=n(U)-n\(A^{c}\)=8-3=5). If the complement is given, subtract it from the total.
Step 3
Exam Tip
(n(A)=n(U)-n\(A^{c}\)=8-3=5)। यदि पूरक दिया हो तो कुल में से पूरक घटाएं।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4\}\) और \(A^{c}\subseteq B\) है, तो (B) में कम से कम कौन से अवयव होने चाहिए?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4\}\), and \(A^{c}\subseteq B\), which elements must at least be in (B)?
#sets
#subset
#complement-application
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A ({1,2,3,4})
B ({5,6,7,8,9,10})
C ({1,3,5,7,9})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
B. ({5,6,7,8,9,10})
Step 1
Concept
\(A^{c}={5,6,7,8,9,10}\), and it is a subset of (B). Hence all these elements must be in (B).
Step 2
Why this answer is correct
The correct answer is B. ({5,6,7,8,9,10}). \(A^{c}={5,6,7,8,9,10}\), and it is a subset of (B). Hence all these elements must be in (B).
Step 3
Exam Tip
\(A^{c}={5,6,7,8,9,10}\), और यह (B) का उपसमुच्चय है। इसलिए ये सभी अवयव (B) में होने जरूरी हैं।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(A=\{2,3,5\}\), तो \(U\setminus A\) किसके बराबर है?
If \(U=\{1,2,3,4,5,6\}\) and \(A=\{2,3,5\}\), what is \(U\setminus A\) equal to?
#sets
#difference
#notation
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A (A)
B \(A^{c}\)
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
B. \(A^{c}\)
Step 1
Concept
\(U\setminus A\) means removing (A) from (U), which is \(A^{c}\). Complement is also written using difference notation.
Step 2
Why this answer is correct
The correct answer is B. \(A^{c}\). \(U\setminus A\) means removing (A) from (U), which is \(A^{c}\). Complement is also written using difference notation.
Step 3
Exam Tip
\(U\setminus A\) का अर्थ है (U) से (A) हटाना, यही \(A^{c}\) है। पूरक को अंतर संकेत से भी लिखते हैं।
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यदि \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,4,7\}\), तो \(A^{c}\cup A\) में कितने अवयव हैं?
If \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,4,7\}\), how many elements are in \(A^{c}\cup A\)?
#sets
#identity
#cardinality
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A (3)
B (4)
C (7)
D (0)
Explanation opens after your attempt
Step 1
Concept
\(A^{c}\cup A=U\), so it has (7) elements. Using the identity directly saves time.
Step 2
Why this answer is correct
The correct answer is C. (7). \(A^{c}\cup A=U\), so it has (7) elements. Using the identity directly saves time.
Step 3
Exam Tip
\(A^{c}\cup A=U\), इसलिए इसमें (7) अवयव हैं। सर्वसमिका को सीधे उपयोग करने से समय बचता है।
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यदि \(U=\{1,2,3,4,5,6,7\}\), \(A=\{2,4,6\}\), तो \(A^{c}\cap A\) में कितने अवयव हैं?
If \(U=\{1,2,3,4,5,6,7\}\), \(A=\{2,4,6\}\), how many elements are in \(A^{c}\cap A\)?
#sets
#disjoint
#cardinality
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A (0)
B (3)
C (4)
D (7)
Explanation opens after your attempt
Step 1
Concept
(A) and \(A^{c}\) are disjoint, so their intersection is empty. The cardinality of the empty set is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). (A) and \(A^{c}\) are disjoint, so their intersection is empty. The cardinality of the empty set is (0).
Step 3
Exam Tip
(A) और \(A^{c}\) में कोई साझा अवयव नहीं होता, इसलिए प्रतिच्छेद खाली है। रिक्त समुच्चय की अवयव संख्या (0) होती है।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,5,8\}\) और \(C=\{3,4,6,7\}\), तो कौन सा कथन सही है?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,5,8\}\), and \(C=\{3,4,6,7\}\), which statement is correct?
#sets
#identify-complement
#reasoning
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A \(C=A^{c}\)
B (C=A)
C (C=U)
D \(C=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(C=A^{c}\)
Step 1
Concept
The elements left in (U) outside (A) are ({3,4,6,7}), which is (C). Compare with (U) to identify a complement.
Step 2
Why this answer is correct
The correct answer is A. \(C=A^{c}\). The elements left in (U) outside (A) are ({3,4,6,7}), which is (C). Compare with (U) to identify a complement.
Step 3
Exam Tip
(A) के बाहर (U) में ({3,4,6,7}) बचते हैं, जो (C) है। पूरक पहचानने के लिए (U) से तुलना करें।
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\(यदि (U={x:x \in \mathbb{N}, 1\le x\le 20}) और (A={x:x \in U,\ x\) 20 का गुणनखंड है\(}), तो (A^{c}) में कितने अवयव होंगे\)?
\(If (U={x:x \in \mathbb{N}, 1\le x\le 20}) and (A={x:x \in U, x\) is a factor of \(20}), how many elements will (A^{c}) have\)?
#sets
#factors
#cardinality
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A (5)
B (6)
C (14)
D (20)
Explanation opens after your attempt
Step 1
Concept
The factors of (20) are ({1,2,4,5,10,20}), so (n(A)=6). Hence (n\(A^{c}\)=20-6=14).
Step 2
Why this answer is correct
The correct answer is C. (14). The factors of (20) are ({1,2,4,5,10,20}), so (n(A)=6). Hence (n\(A^{c}\)=20-6=14).
Step 3
Exam Tip
(20) के गुणनखंड ({1,2,4,5,10,20}) हैं, इसलिए (n(A)=6)। अतः (n\(A^{c}\)=20-6=14)।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,3,5,7,9\}\) और \(B=A^{c}\), तो (B) क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,3,5,7,9\}\), and \(B=A^{c}\), what is (B)?
#sets
#odd-even
#complement
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A ({2,4,6,8,10})
B ({1,3,5,7,9})
C ({1,2,3,4,5})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({2,4,6,8,10})
Step 1
Concept
(A) is the set of odd numbers, so \(A^{c}\) is the even numbers ({2,4,6,8,10}). The pattern can also help.
Step 2
Why this answer is correct
The correct answer is A. ({2,4,6,8,10}). (A) is the set of odd numbers, so \(A^{c}\) is the even numbers ({2,4,6,8,10}). The pattern can also help.
Step 3
Exam Tip
(A) विषम संख्याओं का समुच्चय है, इसलिए \(A^{c}\) सम संख्याएं ({2,4,6,8,10}) हैं। रूप देखकर भी उत्तर मिल सकता है।
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यदि \(U={x:x \in \mathbb{Z}, -3\le x\le 3}\) और \(A=\{-3,-1,1,3\}\), तो \(A^{c}\) क्या है?
If \(U={x:x \in \mathbb{Z}, -3\le x\le 3}\) and \(A=\{-3,-1,1,3\}\), what is \(A^{c}\)?
#sets
#integers
#complement
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A ({-2,0,2})
B ({-3,-1,1,3})
C ({-2,-1,0,1,2})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({-2,0,2})
Step 1
Concept
\(U=\{-3,-2,-1,0,1,2,3\}\), so the elements outside (A) are ({-2,0,2}). Include negative numbers and (0) carefully.
Step 2
Why this answer is correct
The correct answer is A. ({-2,0,2}). \(U=\{-3,-2,-1,0,1,2,3\}\), so the elements outside (A) are ({-2,0,2}). Include negative numbers and (0) carefully.
Step 3
Exam Tip
\(U=\{-3,-2,-1,0,1,2,3\}\), इसलिए (A) से बाहर ({-2,0,2}) हैं। ऋण संख्याओं और (0) को ध्यान से शामिल करें।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4\}\) और \(B=\{5,6,7,8\}\), तो (B) और (A) का संबंध क्या है?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4\}\), and \(B=\{5,6,7,8\}\), what is the relation between (B) and (A)?
#sets
#relation
#complement
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A \(B=A^{c}\)
B (B=A)
C \(B\subset A\)
D \(B\cap A=B\)
Explanation opens after your attempt
Correct Answer
A. \(B=A^{c}\)
Step 1
Concept
(B) contains all elements of (U) that are not in (A). Therefore, \(B=A^{c}\).
Step 2
Why this answer is correct
The correct answer is A. \(B=A^{c}\). (B) contains all elements of (U) that are not in (A). Therefore, \(B=A^{c}\).
Step 3
Exam Tip
(B) में (U) के वे सभी अवयव हैं जो (A) में नहीं हैं। इसलिए \(B=A^{c}\) है।
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यदि \(U=\{1,2,3,4,5\}\) और \(A=\{1,2\}\), तो \(A^{c}\setminus A\) क्या है?
If \(U=\{1,2,3,4,5\}\) and \(A=\{1,2\}\), what is \(A^{c}\setminus A\)?
#sets
#difference
#complement
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A ({3,4,5})
B \(\varnothing\)
C ({1,2})
D (U)
Explanation opens after your attempt
Correct Answer
A. ({3,4,5})
Step 1
Concept
\(A^{c}={3,4,5}\) and it has no element of (A), so the difference remains the same. Subtracting a disjoint set does not change it.
Step 2
Why this answer is correct
The correct answer is A. ({3,4,5}). \(A^{c}={3,4,5}\) and it has no element of (A), so the difference remains the same. Subtracting a disjoint set does not change it.
Step 3
Exam Tip
\(A^{c}={3,4,5}\) और इसमें (A) का कोई अवयव नहीं है, इसलिए अंतर वही रहेगा। असंपाती समुच्चयों में घटाने से समुच्चय नहीं बदलता।
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यदि \(U=\{1,2,3,4,5\}\) और \(A=\{1,2\}\), तो \(A\setminus A^{c}\) क्या है?
If \(U=\{1,2,3,4,5\}\) and \(A=\{1,2\}\), what is \(A\setminus A^{c}\)?
#sets
#set-difference
#identity
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A ({1,2})
B ({3,4,5})
C \(\varnothing\)
D (U)
Explanation opens after your attempt
Correct Answer
A. ({1,2})
Step 1
Concept
(A) and \(A^{c}\) have no common element, so \(A\setminus A^{c}=A\). Use the disjoint property with complements.
Step 2
Why this answer is correct
The correct answer is A. ({1,2}). (A) and \(A^{c}\) have no common element, so \(A\setminus A^{c}=A\). Use the disjoint property with complements.
Step 3
Exam Tip
(A) और \(A^{c}\) में कोई साझा अवयव नहीं है, इसलिए \(A\setminus A^{c}=A\)। पूरक के साथ अंतर में असंपाती गुण उपयोग करें।
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यदि (n\(A^{c}\)=12) और (n(U)=30), तो (n(A)) क्या है?
If (n\(A^{c}\)=12) and (n(U)=30), what is (n(A))?
#sets
#cardinality
#complement
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A (12)
B (18)
C (30)
D (42)
Explanation opens after your attempt
Step 1
Concept
(n(A)=n(U)-n\(A^{c}\)=30-12=18). The cardinalities of a set and its complement add to the total.
Step 2
Why this answer is correct
The correct answer is B. (18). (n(A)=n(U)-n\(A^{c}\)=30-12=18). The cardinalities of a set and its complement add to the total.
Step 3
Exam Tip
(n(A)=n(U)-n\(A^{c}\)=30-12=18)। पूरक और समुच्चय की अवयव संख्या मिलकर कुल देती है।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{2,4,6,8\}\), तो कौन सा कथन सही है?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{2,4,6,8\}\), which statement is correct?
#sets
#membership
#true-statement
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A \(9\in A^{c}\)
B \(2\in A^{c}\)
C \(4\notin A\)
D \(A^{c}={2,4,6,8}\)
Explanation opens after your attempt
Correct Answer
A. \(9\in A^{c}\)
Step 1
Concept
(9) is in (U) and not in (A), so \(9\in A^{c}\). In membership questions, check both conditions.
Step 2
Why this answer is correct
The correct answer is A. \(9\in A^{c}\). (9) is in (U) and not in (A), so \(9\in A^{c}\). In membership questions, check both conditions.
Step 3
Exam Tip
(9) (U) में है और (A) में नहीं है, इसलिए \(9\in A^{c}\)। सदस्यता प्रश्नों में दोनों शर्तें जांचें।
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यदि \(U=\{a,b,c,d,e,f\}\), \(A=\{a,b,c\}\) और \(D=\{d,e,f\}\), तो \(A\cap D\) और \(A\cup D\) के आधार पर कौन सा निष्कर्ष सही है?
If \(U=\{a,b,c,d,e,f\}\), \(A=\{a,b,c\}\), and \(D=\{d,e,f\}\), which conclusion is correct using \(A\cap D\) and \(A\cup D\)?
#sets
#proof-idea
#complement
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A \(D=A^{c}\)
B (D=A)
C \(D=\varnothing\)
D \(D\not\subseteq U\)
Explanation opens after your attempt
Correct Answer
A. \(D=A^{c}\)
Step 1
Concept
\(A\cap D=\varnothing\) and \(A\cup D=U\), so \(D=A^{c}\). These two conditions are useful to prove a complement.
Step 2
Why this answer is correct
The correct answer is A. \(D=A^{c}\). \(A\cap D=\varnothing\) and \(A\cup D=U\), so \(D=A^{c}\). These two conditions are useful to prove a complement.
Step 3
Exam Tip
\(A\cap D=\varnothing\) और \(A\cup D=U\), इसलिए \(D=A^{c}\)। पूरक साबित करने के लिए ये दो शर्तें उपयोगी हैं।
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\(यदि (U={x:x \in \mathbb{N}, x\le 12}) और (A={x:x \in U,\ x\) 2 से विभाज्य नहीं है\(}), तो (A^{c}) क्या है\)?
\(If (U={x:x \in \mathbb{N}, x\le 12}) and (A={x:x \in U, x\) is not divisible by \(2}), what is (A^{c})\)?
#sets
#negative-condition
#even-odd
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A ({1,3,5,7,9,11})
B ({2,4,6,8,10,12})
C ({1,2,3,4,5,6})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
B. ({2,4,6,8,10,12})
Step 1
Concept
(A) contains odd numbers, so the complement contains even numbers. With negative wording, reverse the condition carefully.
Step 2
Why this answer is correct
The correct answer is B. ({2,4,6,8,10,12}). (A) contains odd numbers, so the complement contains even numbers. With negative wording, reverse the condition carefully.
Step 3
Exam Tip
(A) में विषम संख्याएं हैं, इसलिए पूरक में सम संख्याएं हैं। नकारात्मक शब्दों में शर्त को उल्टा समझें।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4,5,6\}\) और \(B=\{4,5,6,7,8\}\), तो (\(A\setminus B\)^{c}) क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4,5,6\}\), and \(B=\{4,5,6,7,8\}\), what is (\(A\setminus B\)^{c})?
#sets
#difference
#complement
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A ({1,2,3})
B ({4,5,6,7,8,9,10})
C ({7,8,9,10})
D ({1,2,3,9,10})
Explanation opens after your attempt
Correct Answer
B. ({4,5,6,7,8,9,10})
Step 1
Concept
\(A\setminus B={1,2,3}\), so its complement is ({4,5,6,7,8,9,10}). First find the difference, then take the complement.
Step 2
Why this answer is correct
The correct answer is B. ({4,5,6,7,8,9,10}). \(A\setminus B={1,2,3}\), so its complement is ({4,5,6,7,8,9,10}). First find the difference, then take the complement.
Step 3
Exam Tip
\(A\setminus B={1,2,3}\), इसलिए इसका पूरक ({4,5,6,7,8,9,10}) है। पहले अंतर निकालें फिर पूरक लें।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6\}\), तो (\(A^{c}\cup B\)^{c}) क्या है?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4\}\), and \(B=\{3,4,5,6\}\), what is (\(A^{c}\cup B\)^{c})?
#sets
#mixed-operation
#complement
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A ({1,2})
B ({7,8})
C ({3,4,5,6,7,8})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,2})
Step 1
Concept
\(A^{c}={5,6,7,8}\) and \(A^{c}\cup B={3,4,5,6,7,8}\), so the complement is ({1,2}). Do not skip steps.
Step 2
Why this answer is correct
The correct answer is A. ({1,2}). \(A^{c}={5,6,7,8}\) and \(A^{c}\cup B={3,4,5,6,7,8}\), so the complement is ({1,2}). Do not skip steps.
Step 3
Exam Tip
\(A^{c}={5,6,7,8}\) और \(A^{c}\cup B={3,4,5,6,7,8}\), इसलिए पूरक ({1,2}) है। चरण न छोड़ें।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{2,3,5,7\}\) और \(B=\{1,4,6,8,9,10\}\), तो कौन सा कथन (A) और (B) के लिए सही है?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{2,3,5,7\}\), and \(B=\{1,4,6,8,9,10\}\), which statement is correct for (A) and (B)?
#sets
#complement-pair
#reasoning
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A \(B=A^{c}\)
B (A=B)
C \(A\cap B=U\)
D \(A\cup B=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(B=A^{c}\)
Step 1
Concept
The elements outside (A) in (U) are exactly the elements of (B), so \(B=A^{c}\). Also, (A) and (B) are disjoint.
Step 2
Why this answer is correct
The correct answer is A. \(B=A^{c}\). The elements outside (A) in (U) are exactly the elements of (B), so \(B=A^{c}\). Also, (A) and (B) are disjoint.
Step 3
Exam Tip
(A) के बाहर (U) में ठीक (B) के अवयव हैं, इसलिए \(B=A^{c}\)। साथ ही (A) और (B) असंपाती हैं।
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