\(यदि (U={1,2,3,\ldots,18}), (A={x:x\) 2 से विभाज्य है\(}) और (B={x:x\) 3 से विभाज्य है\(}) है, तो (A^c\cap B^c) में कितने तत्व होंगे\)?
\(If (U={1,2,3,\ldots,18}), (A={x:x\) is divisible by \(2}), and (B={x:x\) is divisible by \(3}), how many elements are in (A^c\cap B^c)\)?
#sets
#complement
#de_morgan
#counting
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A (6)
B (9)
C (12)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(A^c\cap B^c\) contains numbers divisible by neither (2) nor (3). These numbers 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 divisible by neither (2) nor (3). These numbers are (1,5,7,11,13,17).
Step 3
Exam Tip
\(A^c\cap B^c\) में वे संख्याएं हैं जो न (2) से और न (3) से विभाज्य हैं। ऐसी संख्याएं (1,5,7,11,13,17) हैं।
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यदि \(U={1,2,3,\ldots,16}\), \(A=\{1,4,9,16\}\) और \(B=\{2,4,6,8,10,12,14,16\}\) है, तो (\(A\cup B\)^c) क्या होगा?
If \(U={1,2,3,\ldots,16}\), \(A=\{1,4,9,16\}\), and \(B=\{2,4,6,8,10,12,14,16\}\), what is (\(A\cup B\)^c)?
#sets
#complement
#union
#finite_sets
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A ({3,5,7,11,13,15})
B ({1,4,9,16})
C ({2,4,6,8,10,12,14,16})
D ({1,2,4,6,8,9,10,12,14,16})
Explanation opens after your attempt
Correct Answer
A. ({3,5,7,11,13,15})
Step 1
Concept
First write \(A\cup B={1,2,4,6,8,9,10,12,14,16}\). The remaining elements in (U) form the complement.
Step 2
Why this answer is correct
The correct answer is A. ({3,5,7,11,13,15}). First write \(A\cup B={1,2,4,6,8,9,10,12,14,16}\). The remaining elements in (U) form the complement.
Step 3
Exam Tip
पहले \(A\cup B={1,2,4,6,8,9,10,12,14,16}\) लिखें। (U) में बचे हुए तत्व ही पूरक हैं।
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\(यदि (U={1,2,3,\ldots,20}), (A={x:x\) अभाज्य है\(}) और (B={x:x\) विषम है\(}) है, तो (A^c\cap B) क्या होगा\)?
\(If (U={1,2,3,\ldots,20}), (A={x:x\) is prime\(}), and (B={x:x\) is odd\(}), what is (A^c\cap B)\)?
#sets
#complement
#prime_numbers
#intersection
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A ({1,9,15})
B ({3,5,7,11,13,17,19})
C ({2,4,6,8,10,12,14,16,18,20})
D ({1,3,5,7,9,11,13,15,17,19})
Explanation opens after your attempt
Correct Answer
A. ({1,9,15})
Step 1
Concept
\(A^c\cap B\) contains odd numbers that are not prime. (1), (9), and (15) satisfy this condition.
Step 2
Why this answer is correct
The correct answer is A. ({1,9,15}). \(A^c\cap B\) contains odd numbers that are not prime. (1), (9), and (15) satisfy this condition.
Step 3
Exam Tip
\(A^c\cap B\) में विषम लेकिन अभाज्य नहीं संख्याएं आएंगी। (1), (9) और (15) इस शर्त को पूरा करते हैं।
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यदि \(U={x:x\in\mathbb{Z},-5\le x\le 5}\) और \(A={x:x^2<9}\) है, तो \(A^c\) क्या होगा?
If \(U={x:x\in\mathbb{Z},-5\le x\le 5}\) and \(A={x:x^2<9}\), what is \(A^c\)?
#sets
#complement
#integers
#inequality
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A ({-5,-4,-3,3,4,5})
B ({-2,-1,0,1,2})
C ({-3,-2,-1,0,1,2,3})
D ({-5,-4,4,5})
Explanation opens after your attempt
Correct Answer
A. ({-5,-4,-3,3,4,5})
Step 1
Concept
From \(x^2<9\), \(A=\{-2,-1,0,1,2\}\). Removing these from (U) gives the complement.
Step 2
Why this answer is correct
The correct answer is A. ({-5,-4,-3,3,4,5}). From \(x^2<9\), \(A=\{-2,-1,0,1,2\}\). Removing these from (U) gives the complement.
Step 3
Exam Tip
\(x^2<9\) से \(A=\{-2,-1,0,1,2\}\) मिलता है। (U) से इन्हें हटाने पर पूरक मिलता है।
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यदि (U=[-3,7]) और (A=(-1,4)) है, तो \(A^c\) क्या होगा?
If (U=[-3,7]) and (A=(-1,4)), what is \(A^c\)?
#sets
#complement
#intervals
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A \([-3,-1]\cup[4,7]\)
B ([-3,-1)\cup(4,7])
C ((-1,4))
D ([-3,7])
Explanation opens after your attempt
Correct Answer
A. \([-3,-1]\cup[4,7]\)
Step 1
Concept
(-1) and (4) are not included in (A), so they come in the complement. Pay special attention to open and closed endpoints in intervals.
Step 2
Why this answer is correct
The correct answer is A. \([-3,-1]\cup[4,7]\). (-1) and (4) are not included in (A), so they come in the complement. Pay special attention to open and closed endpoints in intervals.
Step 3
Exam Tip
(-1) और (4) दोनों (A) में शामिल नहीं हैं, इसलिए वे पूरक में आएंगे। अंतरालों में खुले और बंद सिरों पर विशेष ध्यान दें।
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यदि (U=(-4,6]) और (A=[0,2]) है, तो \(A^c\) क्या होगा?
If (U=(-4,6]) and (A=[0,2]), what is \(A^c\)?
#sets
#complement
#interval_complement
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A ((-4,0)\cup(2,6])
B (\(-4,0]\cup[2,6]\)
C ([0,2])
D ((-4,6])
Explanation opens after your attempt
Correct Answer
A. ((-4,0)\cup(2,6])
Step 1
Concept
(0) and (2) are included in (A), so the complement stays outside them. (6) is included in (U), so the right endpoint remains closed.
Step 2
Why this answer is correct
The correct answer is A. ((-4,0)\cup(2,6]). (0) and (2) are included in (A), so the complement stays outside them. (6) is included in (U), so the right endpoint remains closed.
Step 3
Exam Tip
(0) और (2) (A) में शामिल हैं, इसलिए पूरक उनसे बाहर होगा। (6) (U) में शामिल है, इसलिए अंतिम सिरा बंद रहेगा।
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यदि \(A\subseteq B\subseteq C\subseteq U\) है, तो पूरकों के लिए कौन सा संबंध सही है?
If \(A\subseteq B\subseteq C\subseteq U\), which relation is correct for complements?
#sets
#complement
#subset_property
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A \(C^c\subseteq B^c\subseteq A^c\)
B \(A^c\subseteq B^c\subseteq C^c\)
C \(A^c=B^c=C^c\)
D \(A^c\cap C^c=U\)
Explanation opens after your attempt
Correct Answer
A. \(C^c\subseteq B^c\subseteq A^c\)
Step 1
Concept
The order of inclusion reverses after taking complements. Hence the complement of the largest set (C) is the smallest.
Step 2
Why this answer is correct
The correct answer is A. \(C^c\subseteq B^c\subseteq A^c\). The order of inclusion reverses after taking complements. Hence the complement of the largest set (C) is the smallest.
Step 3
Exam Tip
पूरक लेने पर समावेशन का क्रम उलट जाता है। इसलिए सबसे बड़े (C) का पूरक सबसे छोटा होगा।
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यदि \(B^c\subseteq A^c\) है, तो निम्न में से कौन सा निष्कर्ष सही है?
If \(B^c\subseteq A^c\), which conclusion is correct?
#sets
#complement
#reverse_inclusion
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A \(A\subseteq B\)
B \(B\subseteq A\)
C \(A=B^c\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(A\subseteq B\)
Step 1
Concept
Inclusion reverses for complements. Therefore \(B^c\subseteq A^c\) gives \(A\subseteq B\).
Step 2
Why this answer is correct
The correct answer is A. \(A\subseteq B\). Inclusion reverses for complements. Therefore \(B^c\subseteq A^c\) gives \(A\subseteq B\).
Step 3
Exam Tip
पूरकों में समावेशन उलट जाता है। इसलिए \(B^c\subseteq A^c\) से \(A\subseteq B\) मिलता है।
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यदि (n(U)=75), (n(A)=42), (n(B)=38) और (n\(A\cap B\)=20) है, तो (n(\(A\cup B\)^c)) कितना होगा?
If (n(U)=75), (n(A)=42), (n(B)=38), and (n\(A\cap B\)=20), what is (n(\(A\cup B\)^c))?
#sets
#complement
#cardinality
#two_sets
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A (15)
B (60)
C (35)
D (20)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\)=42+38-20=60). Hence (n(\(A\cup B\)^c)=75-60=15).
Step 2
Why this answer is correct
The correct answer is A. (15). (n\(A\cup B\)=42+38-20=60). Hence (n(\(A\cup B\)^c)=75-60=15).
Step 3
Exam Tip
(n\(A\cup B\)=42+38-20=60) है। इसलिए (n(\(A\cup B\)^c)=75-60=15) होगा।
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यदि (n(U)=90), (n\(A^c\)=35), (n\(B^c\)=50) और (n\(A^c\cap B^c\)=18) है, तो (n\(A\cap B\)) कितना होगा?
If (n(U)=90), (n\(A^c\)=35), (n\(B^c\)=50), and (n\(A^c\cap B^c\)=18), what is (n\(A\cap B\))?
#sets
#complement
#de_morgan
#cardinality
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A (23)
B (67)
C (55)
D (18)
Explanation opens after your attempt
Step 1
Concept
(n\(A^c\cup B^c\)=35+50-18=67). By De Morgan, this is (n(\(A\cap B\)^c)), so (n\(A\cap B\)=90-67=23).
Step 2
Why this answer is correct
The correct answer is A. (23). (n\(A^c\cup B^c\)=35+50-18=67). By De Morgan, this is (n(\(A\cap B\)^c)), so (n\(A\cap B\)=90-67=23).
Step 3
Exam Tip
(n\(A^c\cup B^c\)=35+50-18=67) है। डी मॉर्गन से यह (n(\(A\cap B\)^c)) है, इसलिए (n\(A\cap B\)=90-67=23)।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4,5\}\) और \(B=\{4,5,6,7,8\}\) है, तो \(A^c-B^c\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4,5\}\), and \(B=\{4,5,6,7,8\}\), what is \(A^c-B^c\)?
#sets
#complement
#set_difference
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A ({6,7,8})
B ({1,2,3})
C ({9,10})
D ({4,5})
Explanation opens after your attempt
Correct Answer
A. ({6,7,8})
Step 1
Concept
\(A^c-B^c=A^c\cap B\). Since \(A^c={6,7,8,9,10}\), the common part with (B) is ({6,7,8}).
Step 2
Why this answer is correct
The correct answer is A. ({6,7,8}). \(A^c-B^c=A^c\cap B\). Since \(A^c={6,7,8,9,10}\), the common part with (B) is ({6,7,8}).
Step 3
Exam Tip
\(A^c-B^c=A^c\cap B\) होता है। \(A^c={6,7,8,9,10}\), इसलिए (B) के साथ साझा भाग ({6,7,8}) है।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{2,3,5,7\}\) और \(B=\{1,2,3,4,5\}\) है, तो ((B-A)^c) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{2,3,5,7\}\), and \(B=\{1,2,3,4,5\}\), what is ((B-A)^c)?
#sets
#complement
#difference_complement
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A ({2,3,5,6,7,8,9})
B ({1,4})
C ({6,7,8,9})
D ({1,2,3,4,5})
Explanation opens after your attempt
Correct Answer
A. ({2,3,5,6,7,8,9})
Step 1
Concept
First (B-A={1,4}). Removing it from (U) gives ((B-A)^c={2,3,5,6,7,8,9}).
Step 2
Why this answer is correct
The correct answer is A. ({2,3,5,6,7,8,9}). First (B-A={1,4}). Removing it from (U) gives ((B-A)^c={2,3,5,6,7,8,9}).
Step 3
Exam Tip
पहले (B-A={1,4}) है। (U) से इसे हटाने पर ((B-A)^c={2,3,5,6,7,8,9}) मिलता है।
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\(यदि (U={1,2,3,\ldots,40}) और (A={x:x\) 4 या 5 से विभाज्य है\(}) है, तो (n(A^c)) कितना होगा\)?
\(If (U={1,2,3,\ldots,40}) and (A={x:x\) is divisible by 4 or \(5}), what is (n(A^c))\)?
#sets
#complement
#counting
#divisibility
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A (24)
B (16)
C (18)
D (20)
Explanation opens after your attempt
Step 1
Concept
There are (10) multiples of (4) and (8) multiples of (5), with (2) common multiples of (20). Thus (n(A)=10+8-2=16), so (n\(A^c\)=24).
Step 2
Why this answer is correct
The correct answer is A. (24). There are (10) multiples of (4) and (8) multiples of (5), with (2) common multiples of (20). Thus (n(A)=10+8-2=16), so (n\(A^c\)=24).
Step 3
Exam Tip
(4) के (10) और (5) के (8) गुणज हैं, साझा (20) के (2) गुणज हैं। इसलिए (n(A)=10+8-2=16) और (n\(A^c\)=24)।
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\(यदि (U={1,2,3,\ldots,60}) और (A={x:x\) 6 से विभाज्य है\(}) है, तो (n(A^c)) कितना होगा\)?
\(If (U={1,2,3,\ldots,60}) and (A={x:x\) is divisible by \(6}), what is (n(A^c))\)?
#sets
#complement
#multiples
#cardinality
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A (50)
B (10)
C (54)
D (60)
Explanation opens after your attempt
Step 1
Concept
There are (10) multiples of (6) from (1) to (60). Therefore the complement has (60-10=50) elements.
Step 2
Why this answer is correct
The correct answer is A. (50). There are (10) multiples of (6) from (1) to (60). Therefore the complement has (60-10=50) elements.
Step 3
Exam Tip
(1) से (60) तक (6) के (10) गुणज हैं। इसलिए पूरक में (60-10=50) तत्व होंगे।
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\(यदि (U={1,2,3,\ldots,12}) और (A={x:x\in U\) और \(x^2-7x+12=0}) है, तो (A^c) क्या होगा\)?
\(If (U={1,2,3,\ldots,12}) and (A={x:x\in U\) and \(x^2-7x+12=0}), what is (A^c)\)?
#sets
#complement
#quadratic_condition
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A ({1,2,5,6,7,8,9,10,11,12})
B ({3,4})
C ({1,2,3,4,5,6})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,2,5,6,7,8,9,10,11,12})
Step 1
Concept
From \(x^2-7x+12=0\), (x=3,4). Removing (3) and (4) from (U) gives \(A^c\).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,5,6,7,8,9,10,11,12}). From \(x^2-7x+12=0\), (x=3,4). Removing (3) and (4) from (U) gives \(A^c\).
Step 3
Exam Tip
\(x^2-7x+12=0\) से (x=3,4) मिलते हैं। (U) से (3) और (4) हटाने पर \(A^c\) मिलता है।
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यदि \(U={x:x\in\mathbb{Z},-6\le x\le 6}\) और \(A={x:x^2=16}\) है, तो (n\(A^c\)) कितना होगा?
If \(U={x:x\in\mathbb{Z},-6\le x\le 6}\) and \(A={x:x^2=16}\), what is (n\(A^c\))?
#sets
#complement
#integers
#cardinality
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A (11)
B (2)
C (13)
D (9)
Explanation opens after your attempt
Step 1
Concept
There are (13) integers in (U), and \(A=\{-4,4\}\). Hence (n\(A^c\)=13-2=11).
Step 2
Why this answer is correct
The correct answer is A. (11). There are (13) integers in (U), and \(A=\{-4,4\}\). Hence (n\(A^c\)=13-2=11).
Step 3
Exam Tip
(U) में (13) पूर्णांक हैं और \(A=\{-4,4\}\) है। इसलिए (n\(A^c\)=13-2=11) होगा।
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एक सर्वे में (150) लोगों में से (85) चाय पसंद करते हैं, (70) कॉफी पसंद करते हैं और (40) दोनों पसंद करते हैं। न चाय न कॉफी पसंद करने वाले लोगों की संख्या कितनी है?
In a survey of (150) people, (85) like tea, (70) like coffee, and (40) like both. How many people like neither tea nor coffee?
#sets
#complement
#word_problem
#two_sets
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A (35)
B (115)
C (45)
D (40)
Explanation opens after your attempt
Step 1
Concept
People who like tea or coffee are (85+70-40=115). Therefore the complement has (150-115=35) people.
Step 2
Why this answer is correct
The correct answer is A. (35). People who like tea or coffee are (85+70-40=115). Therefore the complement has (150-115=35) people.
Step 3
Exam Tip
चाय या कॉफी पसंद करने वाले (85+70-40=115) हैं। इसलिए पूरक में (150-115=35) लोग होंगे।
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यदि (n(U)=96) और (n\(A^c\)=\frac{1}{3}n(U)) है, तो (n(A)) कितना होगा?
If (n(U)=96) and (n\(A^c\)=\frac{1}{3}n(U)), what is (n(A))?
#sets
#complement
#fraction
#cardinality
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A (64)
B (32)
C (96)
D (48)
Explanation opens after your attempt
Step 1
Concept
(n\(A^c\)=\frac{1}{3}\times 96=32). Therefore (n(A)=96-32=64).
Step 2
Why this answer is correct
The correct answer is A. (64). (n\(A^c\)=\frac{1}{3}\times 96=32). Therefore (n(A)=96-32=64).
Step 3
Exam Tip
(n\(A^c\)=\frac{1}{3}\times 96=32) है। इसलिए (n(A)=96-32=64) होगा।
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\(यदि (U={1,2,3,\ldots,36}) और (A={x:x\) पूर्ण वर्ग है\(}) है, तो (n(A^c)) कितना होगा\)?
\(If (U={1,2,3,\ldots,36}) and (A={x:x\) is a perfect square\(}), what is (n(A^c))\)?
#sets
#complement
#perfect_squares
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A (30)
B (6)
C (29)
D (36)
Explanation opens after your attempt
Step 1
Concept
The perfect squares from (1) to (36) are (1,4,9,16,25,36). Hence (n\(A^c\)=36-6=30).
Step 2
Why this answer is correct
The correct answer is A. (30). The perfect squares from (1) to (36) are (1,4,9,16,25,36). Hence (n\(A^c\)=36-6=30).
Step 3
Exam Tip
(1) से (36) तक पूर्ण वर्ग (1,4,9,16,25,36) हैं। इसलिए (n\(A^c\)=36-6=30) होगा।
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\(यदि (U={1,2,3,\ldots,20}) और (A={x:x\) 4 से विभाज्य है\(}) है, तो (A^c\cap{x:x\) सम है}) क्या होगा?
\(If (U={1,2,3,\ldots,20}) and (A={x:x\) is divisible by \(4}), what is (A^c\cap{x:x\) is even})?
#sets
#complement
#intersection
#divisibility
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A ({2,6,10,14,18})
B ({4,8,12,16,20})
C ({2,4,6,8,10,12,14,16,18,20})
D ({1,3,5,7,9,11,13,15,17,19})
Explanation opens after your attempt
Correct Answer
A. ({2,6,10,14,18})
Step 1
Concept
This is like removing the multiples of (4) from the even numbers. Therefore the answer is (2,6,10,14,18).
Step 2
Why this answer is correct
The correct answer is A. ({2,6,10,14,18}). This is like removing the multiples of (4) from the even numbers. Therefore the answer is (2,6,10,14,18).
Step 3
Exam Tip
यह सम संख्याओं में से (4) से विभाज्य संख्याएं हटाने जैसा है। इसलिए उत्तर (2,6,10,14,18) है।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4,5,6\}\) और \(A^c\subseteq B\subseteq U\) है, तो (B) का न्यूनतम संभव मान क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4,5,6\}\), and \(A^c\subseteq B\subseteq U\), what is the smallest possible value of (B)?
#sets
#complement
#subset
#minimum_set
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A ({7,8,9,10})
B ({1,2,3,4,5,6})
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({7,8,9,10})
Step 1
Concept
The smallest (B) will be exactly \(A^c\). Here \(A^c={7,8,9,10}\).
Step 2
Why this answer is correct
The correct answer is A. ({7,8,9,10}). The smallest (B) will be exactly \(A^c\). Here \(A^c={7,8,9,10}\).
Step 3
Exam Tip
न्यूनतम (B) वही होगा जो \(A^c\) है। यहां \(A^c={7,8,9,10}\) है।
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यदि \(U=\{1,2,3,4,5,6,7\}\) और \(A=\{2,4,6\}\) है, तो ऐसा (B) कौन सा होगा जिससे \(B^c=A\) सत्य हो?
If \(U=\{1,2,3,4,5,6,7\}\) and \(A=\{2,4,6\}\), which (B) makes \(B^c=A\) true?
#sets
#complement
#identify_set
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A ({1,3,5,7})
B ({2,4,6})
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,7})
Step 1
Concept
If \(B^c=A\), then \(B=A^c\). Removing (2,4,6) from (U) gives \(B=\{1,3,5,7\}\).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,7}). If \(B^c=A\), then \(B=A^c\). Removing (2,4,6) from (U) gives \(B=\{1,3,5,7\}\).
Step 3
Exam Tip
यदि \(B^c=A\), तो \(B=A^c\) होगा। (U) से (2,4,6) हटाने पर \(B=\{1,3,5,7\}\) मिलता है।
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यदि \(U=\{a,b,c,d,e,g\}\), \(A=\{a,d,g\}\) और \(B=\{b,c,e\}\) है, तो कौन सा कथन सही है?
If \(U=\{a,b,c,d,e,g\}\), \(A=\{a,d,g\}\), and \(B=\{b,c,e\}\), 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) have no common element 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) have no common element and together form (U). Therefore (B) is the complement of (A).
Step 3
Exam Tip
(A) और (B) में कोई साझा तत्व नहीं है और दोनों मिलकर (U) बनाते हैं। इसलिए (B), (A) का पूरक है।
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यदि \(P\cap Q=\varnothing\) और \(P\cup Q=U\) है, तो \(P^c\) किसके बराबर होगा?
If \(P\cap Q=\varnothing\) and \(P\cup Q=U\), then \(P^c\) is equal to what?
#sets
#complement
#property_check
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A (Q)
B (P)
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
If two sets are disjoint and together form (U), they are complements. Hence \(P^c=Q\).
Step 2
Why this answer is correct
The correct answer is A. (Q). If two sets are disjoint and together form (U), they are complements. Hence \(P^c=Q\).
Step 3
Exam Tip
यदि दो समुच्चय असंबद्ध हों और मिलकर (U) बनाएं, तो वे पूरक होते हैं। इसलिए \(P^c=Q\) होगा।
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यदि \(A\cup A^c=U\) और (n(A)=27), (n\(A^c\)=33) है, तो (n(U)) कितना होगा?
If \(A\cup A^c=U\), (n(A)=27), and (n\(A^c\)=33), what is (n(U))?
#sets
#complement
#cardinality_property
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A (60)
B (6)
C (33)
D (27)
Explanation opens after your attempt
Step 1
Concept
(A) and \(A^c\) are disjoint and form (U). Therefore (n(U)=27+33=60).
Step 2
Why this answer is correct
The correct answer is A. (60). (A) and \(A^c\) are disjoint and form (U). Therefore (n(U)=27+33=60).
Step 3
Exam Tip
(A) और \(A^c\) असंबद्ध होकर (U) बनाते हैं। इसलिए (n(U)=27+33=60) होगा।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,3,4,5,6\}\) है, तो (\(A^c\)^c\cap{3,6,9}) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,3,4,5,6\}\), what is (\(A^c\)^c\cap{3,6,9})?
#sets
#complement
#double_complement
#intersection
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A ({3,6})
B ({9})
C ({3,6,9})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({3,6})
Step 1
Concept
(\(A^c\)^c=A). Therefore \(A\cap{3,6,9}={3,6}\).
Step 2
Why this answer is correct
The correct answer is A. ({3,6}). (\(A^c\)^c=A). Therefore \(A\cap{3,6,9}={3,6}\).
Step 3
Exam Tip
(\(A^c\)^c=A) होता है। इसलिए \(A\cap{3,6,9}={3,6}\) मिलेगा।
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यदि \(U={1,2,3,\ldots,12}\) और \(A=\{3,6,9,12\}\) है, तो \(A^c\cup{6,12}\) में कितने तत्व होंगे?
If \(U={1,2,3,\ldots,12}\) and \(A=\{3,6,9,12\}\), how many elements are in \(A^c\cup{6,12}\)?
#sets
#complement
#cardinality
#union
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A (10)
B (8)
C (12)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(A^c\) has (8) elements, and (6,12) are not in it. Adding these two new elements gives (10) elements.
Step 2
Why this answer is correct
The correct answer is A. (10). \(A^c\) has (8) elements, and (6,12) are not in it. Adding these two new elements gives (10) elements.
Step 3
Exam Tip
\(A^c\) में (8) तत्व हैं और (6,12) इसमें नहीं हैं। इसलिए दो नए तत्व जोड़ने पर कुल (10) तत्व होंगे।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\) और \(A=\{1,5,10\}\) है, तो \(A^c-{2,3,4}\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A=\{1,5,10\}\), what is \(A^c-{2,3,4}\)?
#sets
#complement
#set_difference
#application
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A ({6,7,8,9})
B ({2,3,4,6,7,8,9})
C ({1,5,10})
D ({2,3,4})
Explanation opens after your attempt
Correct Answer
A. ({6,7,8,9})
Step 1
Concept
\(A^c={2,3,4,6,7,8,9}\). Removing (2,3,4) leaves ({6,7,8,9}).
Step 2
Why this answer is correct
The correct answer is A. ({6,7,8,9}). \(A^c={2,3,4,6,7,8,9}\). Removing (2,3,4) leaves ({6,7,8,9}).
Step 3
Exam Tip
\(A^c={2,3,4,6,7,8,9}\) है। इसमें से (2,3,4) हटाने पर ({6,7,8,9}) बचता है।
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\(यदि (U={x:x\) एक अंक है\(}) और (A={x:x\) अभाज्य अंक है\(}), तो (n(A^c)) कितना होगा\)?
\(If (U={x:x\) is a digit\(}) and (A={x:x\) is a prime digit\(}), what is (n(A^c))\)?
#sets
#complement
#digits
#counting
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A (6)
B (4)
C (10)
D (5)
Explanation opens after your attempt
Step 1
Concept
The prime digits are (2,3,5,7). There are (10) digits in all, so the complement has (10-4=6) digits.
Step 2
Why this answer is correct
The correct answer is A. (6). The prime digits are (2,3,5,7). There are (10) digits in all, so the complement has (10-4=6) digits.
Step 3
Exam Tip
अंकों में अभाज्य अंक (2,3,5,7) हैं। कुल (10) अंक हैं, इसलिए पूरक में (10-4=6) अंक होंगे।
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\(यदि (U={1,2,3,\ldots,18}) और (A={x:x\) 2 और 5 दोनों से विभाज्य है\(}), तो (A^c) क्या होगा\)?
\(If (U={1,2,3,\ldots,18}) and (A={x:x\) is divisible by both 2 and \(5}), what is (A^c)\)?
#sets
#complement
#divisibility
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A ({1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18})
B ({10})
C ({2,4,5,6,8,10,12,14,15,16,18})
D ({1,3,7,9,11,13,17})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18})
Step 1
Concept
Divisible by both means divisible by (10). From (1) to (18), only (10) satisfies this, so all others are in \(A^c\).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18}). Divisible by both means divisible by (10). From (1) to (18), only (10) satisfies this, so all others are in \(A^c\).
Step 3
Exam Tip
दोनों से विभाज्य होने का अर्थ (10) से विभाज्य होना है। (1) से (18) तक केवल (10) ऐसा है, इसलिए बाकी सभी \(A^c\) में हैं।
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यदि \(U={1,2,3,\ldots,10}\), \(A=\{2,4,6,8,10\}\) और \(C=A^c\) है, तो \(C^c\cap{1,2,3,4}\) क्या होगा?
If \(U={1,2,3,\ldots,10}\), \(A=\{2,4,6,8,10\}\), and \(C=A^c\), what is \(C^c\cap{1,2,3,4}\)?
#sets
#complement
#double_complement
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A ({2,4})
B ({1,3})
C ({1,2,3,4})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({2,4})
Step 1
Concept
\(C=A^c\), so \(C^c=A\). Now \(A\cap{1,2,3,4}={2,4}\).
Step 2
Why this answer is correct
The correct answer is A. ({2,4}). \(C=A^c\), so \(C^c=A\). Now \(A\cap{1,2,3,4}={2,4}\).
Step 3
Exam Tip
\(C=A^c\) है, इसलिए \(C^c=A\) होगा। अब \(A\cap{1,2,3,4}={2,4}\) है।
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किस कथन से यह सिद्ध होता है कि (A) और \(A^c\) मिलकर (U) का विभाजन बनाते हैं?
Which statement proves that (A) and \(A^c\) together form a partition of (U)?
#sets
#complement
#partition
#concept
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A \(A\cap A^c=\varnothing\) और \(A\cup A^c=U\) / \(A\cap A^c=\varnothing\) and \(A\cup A^c=U\)
B \(A\cap A^c=U\) और \(A\cup A^c=\varnothing\) / \(A\cap A^c=U\) and \(A\cup A^c=\varnothing\)
C \(A=A^c\)
D \(A\subseteq A^c\)
Explanation opens after your attempt
Correct Answer
A. \(A\cap A^c=\varnothing\) और \(A\cup A^c=U\) / \(A\cap A^c=\varnothing\) and \(A\cup A^c=U\)
Step 1
Concept
For a partition, the parts must be disjoint and their union must be the whole (U). (A) and \(A^c\) satisfy both conditions.
Step 2
Why this answer is correct
The correct answer is A. \(A\cap A^c=\varnothing\) और \(A\cup A^c=U\) / \(A\cap A^c=\varnothing\) and \(A\cup A^c=U\). For a partition, the parts must be disjoint and their union must be the whole (U). (A) and \(A^c\) satisfy both conditions.
Step 3
Exam Tip
विभाजन के लिए भाग असंबद्ध होने चाहिए और उनका संघ पूरा (U) होना चाहिए। (A) और \(A^c\) यही दोनों शर्तें पूरी करते हैं।
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यदि \(U\ne\varnothing\) है, तो \(A=A^c\) के बारे में कौन सा कथन सही है?
If \(U\ne\varnothing\), which statement about \(A=A^c\) is correct?
#sets
#complement
#reasoning
#impossible
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A ऐसा कोई (A) संभव नहीं है / no such (A) is possible
B यह हर (A) के लिए सही है / it is true for every (A)
C यह केवल (A=U) पर सही है / it is true only for (A=U)
D यह केवल \(A=\varnothing\) पर सही है / it is true only for \(A=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ऐसा कोई (A) संभव नहीं है / no such (A) is possible
Step 1
Concept
If \(A=A^c\), then \(A\cap A^c=A\), but \(A\cap A^c=\varnothing\). For \(U\ne\varnothing\), this situation is impossible.
Step 2
Why this answer is correct
The correct answer is A. ऐसा कोई (A) संभव नहीं है / no such (A) is possible. If \(A=A^c\), then \(A\cap A^c=A\), but \(A\cap A^c=\varnothing\). For \(U\ne\varnothing\), this situation is impossible.
Step 3
Exam Tip
यदि \(A=A^c\), तो \(A\cap A^c=A\) होगा, पर \(A\cap A^c=\varnothing\) है। \(U\ne\varnothing\) में यह स्थिति संभव नहीं होती।
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यदि (U) बड़ा कर दिया जाए और (A) वही रहे, तो \(A^c\) पर क्या प्रभाव पड़ सकता है?
If (U) is enlarged and (A) remains the same, what may happen to \(A^c\)?
#sets
#complement
#universal_set_dependency
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A \(A^c\) में नए तत्व जुड़ सकते हैं / new elements may be added to \(A^c\)
B \(A^c\) हमेशा खाली हो जाएगा / \(A^c\) will always become empty
C \(A^c=A\) हमेशा होगा / \(A^c=A\) will always hold
D \(A^c\) पर कोई प्रभाव नहीं पड़ेगा / \(A^c\) will never be affected
Explanation opens after your attempt
Correct Answer
A. \(A^c\) में नए तत्व जुड़ सकते हैं / new elements may be added to \(A^c\)
Step 1
Concept
Complement depends on (U). If new elements enter (U) and are not in (A), they are added to \(A^c\).
Step 2
Why this answer is correct
The correct answer is A. \(A^c\) में नए तत्व जुड़ सकते हैं / new elements may be added to \(A^c\). Complement depends on (U). If new elements enter (U) and are not in (A), they are added to \(A^c\).
Step 3
Exam Tip
पूरक (U) पर निर्भर करता है। यदि (U) में नए तत्व आए और वे (A) में न हों, तो वे \(A^c\) में जुड़ेंगे।
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यदि \(U_1={1,2,3,4,5}\), \(U_2={1,2,3,4,5,6,7}\) और \(A=\{2,5\}\) है, तो \(U_2\) के सापेक्ष \(A^c\) में \(U_1\) के सापेक्ष \(A^c\) से कौन से अतिरिक्त तत्व होंगे?
If \(U_1={1,2,3,4,5}\), \(U_2={1,2,3,4,5,6,7}\), and \(A=\{2,5\}\), which extra elements are in \(A^c\) relative to \(U_2\) compared with \(A^c\) relative to \(U_1\)?
#sets
#complement
#universal_dependency
#difference
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A ({6,7})
B ({1,3,4})
C ({2,5})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({6,7})
Step 1
Concept
Relative to \(U_1\), the complement is ({1,3,4}), and relative to \(U_2\), it is ({1,3,4,6,7}). The extra elements are ({6,7}).
Step 2
Why this answer is correct
The correct answer is A. ({6,7}). Relative to \(U_1\), the complement is ({1,3,4}), and relative to \(U_2\), it is ({1,3,4,6,7}). The extra elements are ({6,7}).
Step 3
Exam Tip
\(U_1\) में पूरक ({1,3,4}) और \(U_2\) में पूरक ({1,3,4,6,7}) है। अतिरिक्त तत्व ({6,7}) हैं।
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यदि \(U={1,2,3,\ldots,12}\), \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6,7\}\) है, तो (\(A^c\cap B\)^c) क्या होगा?
If \(U={1,2,3,\ldots,12}\), \(A=\{1,2,3,4\}\), and \(B=\{3,4,5,6,7\}\), what is (\(A^c\cap B\)^c)?
#sets
#complement
#nested_operations
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A ({1,2,3,4,8,9,10,11,12})
B ({5,6,7})
C ({1,2,8,9,10,11,12})
D ({3,4,5,6,7})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4,8,9,10,11,12})
Step 1
Concept
\(A^c={5,6,7,8,9,10,11,12}\) and \(A^c\cap B={5,6,7}\). Its complement is (U-{5,6,7}).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4,8,9,10,11,12}). \(A^c={5,6,7,8,9,10,11,12}\) and \(A^c\cap B={5,6,7}\). Its complement is (U-{5,6,7}).
Step 3
Exam Tip
\(A^c={5,6,7,8,9,10,11,12}\) और \(A^c\cap B={5,6,7}\) है। इसका पूरक (U-{5,6,7}) होगा।
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यदि \(U={1,2,3,\ldots,10}\), \(A=\{2,4,6,8,10\}\) और \(B=\{1,2,3,4,5\}\) है, तो (\(A^c\cup B\)^c) क्या होगा?
If \(U={1,2,3,\ldots,10}\), \(A=\{2,4,6,8,10\}\), and \(B=\{1,2,3,4,5\}\), what is (\(A^c\cup B\)^c)?
#sets
#complement
#nested_union
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A ({6,8,10})
B ({1,2,3,4,5,7,9})
C ({7,9})
D ({2,4})
Explanation opens after your attempt
Correct Answer
A. ({6,8,10})
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 (6,8,10).
Step 2
Why this answer is correct
The correct answer is A. ({6,8,10}). \(A^c={1,3,5,7,9}\), and \(A^c\cup B={1,2,3,4,5,7,9}\). The remaining elements in (U) are (6,8,10).
Step 3
Exam Tip
\(A^c={1,3,5,7,9}\) और \(A^c\cup B={1,2,3,4,5,7,9}\) है। (U) में बचे (6,8,10) हैं।
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\(यदि (U={1,2,3,\ldots,24}), (A={x:x\) 4 से विभाज्य है\(}) और (B={x:x\) 6 से विभाज्य है\(}) है, तो (A^c\cap B^c) में कितने तत्व होंगे\)?
\(If (U={1,2,3,\ldots,24}), (A={x:x\) is divisible by \(4}), and (B={x:x\) is divisible by \(6}), how many elements are in (A^c\cap B^c)\)?
#sets
#complement
#counting
#de_morgan
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A (16)
B (8)
C (14)
D (18)
Explanation opens after your attempt
Step 1
Concept
(A^c\cap B^c=\(A\cup B\)^c). Numbers divisible by (4) or (6) are (6+4-2=8), so the complement has (24-8=16) elements.
Step 2
Why this answer is correct
The correct answer is A. (16). (A^c\cap B^c=\(A\cup B\)^c). Numbers divisible by (4) or (6) are (6+4-2=8), so the complement has (24-8=16) elements.
Step 3
Exam Tip
(A^c\cap B^c=\(A\cup B\)^c) है। (4) या (6) से विभाज्य संख्याएं (6+4-2=8) हैं, इसलिए पूरक में (24-8=16) तत्व हैं।
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यदि \(U={1,2,3,\ldots,15}\), \(A=\{1,2,3,4,5\}\) और \(B=\{3,5,7,9,11\}\) है, तो \(A^c\cup B^c\) में कितने तत्व होंगे?
If \(U={1,2,3,\ldots,15}\), \(A=\{1,2,3,4,5\}\), and \(B=\{3,5,7,9,11\}\), how many elements are in \(A^c\cup B^c\)?
#sets
#complement
#cardinality
#de_morgan
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A (13)
B (2)
C (10)
D (15)
Explanation opens after your attempt
Step 1
Concept
(A^c\cup B^c=\(A\cap B\)^c). Since \(A\cap B={3,5}\), the complement has (15-2=13) elements.
Step 2
Why this answer is correct
The correct answer is A. (13). (A^c\cup B^c=\(A\cap B\)^c). Since \(A\cap B={3,5}\), the complement has (15-2=13) elements.
Step 3
Exam Tip
(A^c\cup B^c=\(A\cap B\)^c) है। \(A\cap B={3,5}\), इसलिए पूरक में (15-2=13) तत्व होंगे।
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यदि \(U={1,2,3,\ldots,11}\), \(A=\{1,4,7,10\}\) और \(B=\{2,4,6,8,10\}\) है, तो \(A^c\cap B^c\) क्या होगा?
If \(U={1,2,3,\ldots,11}\), \(A=\{1,4,7,10\}\), and \(B=\{2,4,6,8,10\}\), what is \(A^c\cap B^c\)?
#sets
#complement
#finite
#de_morgan
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A ({3,5,9,11})
B ({1,2,4,6,7,8,10})
C ({4,10})
D ({3,5,7,9,11})
Explanation opens after your attempt
Correct Answer
A. ({3,5,9,11})
Step 1
Concept
(A^c\cap B^c=\(A\cup B\)^c). Since \(A\cup B={1,2,4,6,7,8,10}\), the remaining elements are ({3,5,9,11}).
Step 2
Why this answer is correct
The correct answer is A. ({3,5,9,11}). (A^c\cap B^c=\(A\cup B\)^c). Since \(A\cup B={1,2,4,6,7,8,10}\), the remaining elements are ({3,5,9,11}).
Step 3
Exam Tip
(A^c\cap B^c=\(A\cup B\)^c) है। \(A\cup B={1,2,4,6,7,8,10}\), इसलिए बचे तत्व ({3,5,9,11}) हैं।
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यदि \(U={1,2,3,\ldots,14}\) और \(A^c={2,3,5,7,11,13}\) है, तो (A) में कितने तत्व होंगे?
If \(U={1,2,3,\ldots,14}\) and \(A^c={2,3,5,7,11,13}\), how many elements are in (A)?
#sets
#complement
#reverse_cardinality
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A (8)
B (6)
C (14)
D (20)
Explanation opens after your attempt
Step 1
Concept
(U) has (14) elements and \(A^c\) has (6) elements. Therefore (n(A)=14-6=8).
Step 2
Why this answer is correct
The correct answer is A. (8). (U) has (14) elements and \(A^c\) has (6) elements. Therefore (n(A)=14-6=8).
Step 3
Exam Tip
(U) में (14) तत्व हैं और \(A^c\) में (6) तत्व हैं। इसलिए (n(A)=14-6=8) होगा।
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यदि (n(U)=84) और (n(A)=2n\(A^c\)) है, तो (n\(A^c\)) कितना होगा?
If (n(U)=84) and (n(A)=2n\(A^c\)), what is (n\(A^c\))?
#sets
#complement
#algebra
#cardinality
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A (28)
B (56)
C (42)
D (21)
Explanation opens after your attempt
Step 1
Concept
Let (n\(A^c\)=x), then (n(A)=2x). Thus (2x+x=84), giving (x=28).
Step 2
Why this answer is correct
The correct answer is A. (28). Let (n\(A^c\)=x), then (n(A)=2x). Thus (2x+x=84), giving (x=28).
Step 3
Exam Tip
मान लें (n\(A^c\)=x), तब (n(A)=2x)। इसलिए (2x+x=84) से (x=28) मिलेगा।
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यदि (n(U)=72) और (n\(A^c\)=3n(A)) है, तो (n(A)) कितना होगा?
If (n(U)=72) and (n\(A^c\)=3n(A)), what is (n(A))?
#sets
#complement
#algebraic_count
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A (18)
B (54)
C (24)
D (36)
Explanation opens after your attempt
Step 1
Concept
Let (n(A)=x), then (n\(A^c\)=3x). Hence (x+3x=72), so (x=18).
Step 2
Why this answer is correct
The correct answer is A. (18). Let (n(A)=x), then (n\(A^c\)=3x). Hence (x+3x=72), so (x=18).
Step 3
Exam Tip
मान लें (n(A)=x), तब (n\(A^c\)=3x)। इसलिए (x+3x=72) से (x=18) है।
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\(यदि (A^c={x:x\in U\) और \(x\notin A}) है, तो (A\cup A^c=U) क्यों होता है\)?
\(If (A^c={x:x\in U\) and \(x\notin A}), why is (A\cup A^c=U)\)?
#sets
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#conceptual_reasoning
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A क्योंकि (U) का हर तत्व या तो (A) में है या (A) के बाहर है / because every element of (U) is either in (A) or outside (A)
B क्योंकि (A) हमेशा खाली है / because (A) is always empty
C क्योंकि \(A^c\) हमेशा खाली है / because \(A^c\) is always empty
D क्योंकि \(A=U^c\) हमेशा है / because \(A=U^c\) always
Explanation opens after your attempt
Correct Answer
A. क्योंकि (U) का हर तत्व या तो (A) में है या (A) के बाहर है / because every element of (U) is either in (A) or outside (A)
Step 1
Concept
Every element of (U) must belong to (A) or to \(A^c\). Therefore their union forms the whole (U).
Step 2
Why this answer is correct
The correct answer is A. क्योंकि (U) का हर तत्व या तो (A) में है या (A) के बाहर है / because every element of (U) is either in (A) or outside (A). Every element of (U) must belong to (A) or to \(A^c\). Therefore their union forms the whole (U).
Step 3
Exam Tip
(U) का हर तत्व (A) में या \(A^c\) में जरूर आएगा। इसलिए दोनों का संघ पूरा (U) बनाता है।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\) और \(A=\{2,3,5\}\) है, तो कौन सा (B), (A) का पूरक नहीं है?
If \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(A=\{2,3,5\}\), which (B) is not the complement of (A)?
#sets
#complement
#error_detection
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A ({1,4,6,7,8})
B ({1,4,6,7,8,9})
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. ({1,4,6,7,8})
Step 1
Concept
The correct complement is ({1,4,6,7,8,9}). The option ({1,4,6,7,8}) misses (9).
Step 2
Why this answer is correct
The correct answer is A. ({1,4,6,7,8}). The correct complement is ({1,4,6,7,8,9}). The option ({1,4,6,7,8}) misses (9).
Step 3
Exam Tip
सही पूरक ({1,4,6,7,8,9}) है। विकल्प ({1,4,6,7,8}) में (9) छूट गया है।
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\(यदि (U={1,2,3,\ldots,80}) और (A={x:x\) 8 से विभाज्य है\(}) है, तो (A^c) में कितने तत्व होंगे\)?
\(If (U={1,2,3,\ldots,80}) and (A={x:x\) is divisible by \(8}), how many elements are in (A^c)\)?
#sets
#complement
#multiples
#counting
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A (70)
B (10)
C (72)
D (80)
Explanation opens after your attempt
Step 1
Concept
There are (10) multiples of (8) from (1) to (80). Therefore the complement has (80-10=70) elements.
Step 2
Why this answer is correct
The correct answer is A. (70). There are (10) multiples of (8) from (1) to (80). Therefore the complement has (80-10=70) elements.
Step 3
Exam Tip
(1) से (80) तक (8) के (10) गुणज हैं। इसलिए पूरक में (80-10=70) तत्व होंगे।
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यदि \(U={1,2,3,\ldots,12}\), \(A=\{2,3,5,7,11\}\) और \(B=A^c\) है, तो \(A\cup B\) क्या होगा?
If \(U={1,2,3,\ldots,12}\), \(A=\{2,3,5,7,11\}\), and \(B=A^c\), what is \(A\cup B\)?
#sets
#complement
#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 basic 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 basic property of complement.
Step 3
Exam Tip
यदि \(B=A^c\), तो \(A\cup B=A\cup A^c=U\) होगा। यह पूरक का मूल गुण है।
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यदि \(U={1,2,3,\ldots,12}\), \(A=\{3,6,9,12\}\) और \(B=A^c\) है, तो \(A\cap B\) क्या होगा?
If \(U={1,2,3,\ldots,12}\), \(A=\{3,6,9,12\}\), and \(B=A^c\), what is \(A\cap B\)?
#sets
#complement
#intersection_property
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A \(\varnothing\)
B (U)
C (A)
D (B)
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\)
Step 1
Concept
If \(B=A^c\), then \(A\cap B=A\cap A^c=\varnothing\). Complementary sets are 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 disjoint.
Step 3
Exam Tip
यदि \(B=A^c\), तो \(A\cap B=A\cap A^c=\varnothing\) होगा। पूरक समुच्चय असंबद्ध होते हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4,5\}\) और \(B=\{6,7,8\}\) है, तो (\(A\cup B\)^c) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4,5\}\), and \(B=\{6,7,8\}\), what is (\(A\cup B\)^c)?
#sets
#complement
#union_complement
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A \(\varnothing\)
B (U)
C (A)
D (B)
Explanation opens after your attempt
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 \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,3,5,7\}\) और \(B=\{2,4,6\}\) है, तो (\(A\cap B\)^c) क्या होगा?
If \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,3,5,7\}\), and \(B=\{2,4,6\}\), what is (\(A\cap B\)^c)?
#sets
#complement
#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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