यदि सार्वत्रिक समुच्चय \(U=\{1,2,3,4,5\}\) और \(A=\{1,3\}\) है, तो \(A^c\) क्या होगा?
If the universal set is \(U=\{1,2,3,4,5\}\) and \(A=\{1,3\}\), what is \(A^c\)?
#sets
#complement
#finite_sets
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A ({2,4,5})
B ({1,3})
C ({1,2,3})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({2,4,5})
Step 1
Concept
\(A^c\) contains the elements of (U) that are not in (A). In exams, first remove the elements of (A) from (U).
Step 2
Why this answer is correct
The correct answer is A. ({2,4,5}). \(A^c\) contains the elements of (U) that are not in (A). In exams, first remove the elements of (A) from (U).
Step 3
Exam Tip
\(A^c\) में (U) के वे तत्व आते हैं जो (A) में नहीं हैं। परीक्षा में पहले (U) से (A) के तत्व हटाएं।
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यदि \(U=\{a,b,c,d\}\) और \(A=\{b,d\}\) है, तो \(A^c\) ज्ञात कीजिए।
If \(U=\{a,b,c,d\}\) and \(A=\{b,d\}\), find \(A^c\).
#sets
#complement
#letters
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A ({a,c})
B ({b,d})
C ({a,b})
D ({c,d})
Explanation opens after your attempt
Correct Answer
A. ({a,c})
Step 1
Concept
(A) has (b) and (d), so the remaining elements (a) and (c) are in the complement. While choosing an option, use only elements of (U).
Step 2
Why this answer is correct
The correct answer is A. ({a,c}). (A) has (b) and (d), so the remaining elements (a) and (c) are in the complement. While choosing an option, use only elements of (U).
Step 3
Exam Tip
(A) में (b) और (d) हैं, इसलिए बचे हुए तत्व (a) और (c) पूरक में आएंगे। विकल्प चुनते समय केवल (U) के तत्व देखें।
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समुच्चय (A) के पूरक का सही सूत्र कौन सा है?
Which formula correctly represents the complement of set (A)?
#sets
#complement
#formula
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A \(A^c=U-A\)
B \(A^c=A-U\)
C \(A^c=A\cap U\)
D \(A^c=A\cup U\)
Explanation opens after your attempt
Correct Answer
A. \(A^c=U-A\)
Step 1
Concept
\(A^c\) means removing (A) from (U). Always remember the formula \(A^c=U-A\).
Step 2
Why this answer is correct
The correct answer is A. \(A^c=U-A\). \(A^c\) means removing (A) from (U). Always remember the formula \(A^c=U-A\).
Step 3
Exam Tip
\(A^c\) का अर्थ है (U) में से (A) को हटाना। सूत्र \(A^c=U-A\) को हमेशा याद रखें।
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यदि \(x\in U\) और \(x\notin A\) है, तो (x) किस समुच्चय का तत्व होगा?
If \(x\in U\) and \(x\notin A\), then (x) will be an element of which set?
#sets
#complement
#membership
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A \(A^c\) / complement of (A)
B (A) / set (A)
C \(\varnothing\) / empty set
D \(A\cap A^c\) / intersection \(A\cap A^c\)
Explanation opens after your attempt
Correct Answer
A. \(A^c\) / complement of (A)
Step 1
Concept
An element that is in (U) but not in (A) belongs to \(A^c\). For membership questions, apply the definition directly.
Step 2
Why this answer is correct
The correct answer is A. \(A^c\) / complement of (A). An element that is in (U) but not in (A) belongs to \(A^c\). For membership questions, apply the definition directly.
Step 3
Exam Tip
जो तत्व (U) में हो लेकिन (A) में न हो, वह \(A^c\) में होता है। सदस्यता वाले प्रश्नों में परिभाषा सीधे लगाएं।
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यदि \(U=\{2,4,6,8\}\) और (A=U) है, तो \(A^c\) क्या होगा?
If \(U=\{2,4,6,8\}\) and (A=U), what is \(A^c\)?
#sets
#complement
#universal_set
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A \(\varnothing\) / empty set
B (U) / universal set
C ({2,4})
D ({6,8})
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\) / empty set
Step 1
Concept
When (A=U), no element of (U) remains outside (A). Hence the complement is \(\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\) / empty set. When (A=U), no element of (U) remains outside (A). Hence the complement is \(\varnothing\).
Step 3
Exam Tip
जब (A=U) होता है, तब (U) में (A) से बाहर कोई तत्व नहीं बचता। इसलिए पूरक \(\varnothing\) होता है।
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यदि \(U=\{1,2,3\}\) और \(A=\varnothing\) है, तो \(A^c\) क्या होगा?
If \(U=\{1,2,3\}\) and \(A=\varnothing\), what is \(A^c\)?
#sets
#complement
#empty_set
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A (U) / universal set
B \(\varnothing\) / empty set
C ({1})
D ({2,3})
Explanation opens after your attempt
Correct Answer
A. (U) / universal set
Step 1
Concept
\(\varnothing\) has no element, so all elements of (U) come in the complement. Remember that \(\varnothing^c=U\).
Step 2
Why this answer is correct
The correct answer is A. (U) / universal set. \(\varnothing\) has no element, so all elements of (U) come in the complement. Remember that \(\varnothing^c=U\).
Step 3
Exam Tip
\(\varnothing\) में कोई तत्व नहीं होता, इसलिए (U) के सभी तत्व पूरक में आते हैं। याद रखें कि \(\varnothing^c=U\) होता है।
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यदि (n(U)=20) और (n(A)=7) है, तो (n\(A^c\)) कितना होगा?
If (n(U)=20) and (n(A)=7), what is (n\(A^c\))?
#sets
#complement
#counting
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A (13)
B (27)
C (7)
D (20)
Explanation opens after your attempt
Step 1
Concept
If \(A\subseteq U\), then (n\(A^c\)=n(U)-n(A)). Therefore (20-7=13).
Step 2
Why this answer is correct
The correct answer is A. (13). If \(A\subseteq U\), then (n\(A^c\)=n(U)-n(A)). Therefore (20-7=13).
Step 3
Exam Tip
यदि \(A\subseteq U\) है, तो (n\(A^c\)=n(U)-n(A)) होता है। इसलिए (20-7=13) होगा।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(A^c={5,6}\) है, तो (A) क्या होगा?
If \(U=\{1,2,3,4,5,6\}\) and \(A^c={5,6}\), what is (A)?
#sets
#complement
#reverse_finding
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A ({1,2,3,4})
B ({5,6})
C ({1,5,6})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4})
Step 1
Concept
(A) and \(A^c\) together make the whole (U). So (A) has all elements except (5) and (6).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4}). (A) and \(A^c\) together make the whole (U). So (A) has all elements except (5) and (6).
Step 3
Exam Tip
(A) और \(A^c\) मिलकर पूरा (U) बनाते हैं। इसलिए (A) में (5) और (6) को छोड़कर बाकी तत्व होंगे।
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किसी भी समुच्चय (A) के लिए \(A\cup A^c\) किसके बराबर होता है?
For any set (A), \(A\cup A^c\) is equal to what?
#sets
#complement
#union_property
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A (U) / universal set
B \(\varnothing\) / empty set
C (A) / set (A)
D \(A^c\) / complement of (A)
Explanation opens after your attempt
Correct Answer
A. (U) / universal set
Step 1
Concept
All elements of (A) and \(A^c\) together form (U). This is one of the most important properties of complement.
Step 2
Why this answer is correct
The correct answer is A. (U) / universal set. All elements of (A) and \(A^c\) together form (U). This is one of the most important properties of complement.
Step 3
Exam Tip
(A) और \(A^c\) के सभी तत्व मिलकर (U) बनाते हैं। यह पूरक का सबसे महत्वपूर्ण गुण है।
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किसी भी समुच्चय (A) के लिए \(A\cap A^c\) किसके बराबर होता है?
For any set (A), \(A\cap A^c\) is equal to what?
#sets
#complement
#intersection_property
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A \(\varnothing\) / empty set
B (U) / universal set
C (A) / set (A)
D \(A^c\) / complement of (A)
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\) / empty set
Step 1
Concept
No element can be both in (A) and outside (A) at the same time. Hence \(A\cap A^c=\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\) / empty set. No element can be both in (A) and outside (A) at the same time. Hence \(A\cap A^c=\varnothing\).
Step 3
Exam Tip
कोई तत्व एक साथ (A) में और (A) के बाहर नहीं हो सकता। इसलिए \(A\cap A^c=\varnothing\) होता है।
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किसी भी समुच्चय (A) के लिए (\(A^c\)^c) किसके बराबर होता है?
For any set (A), (\(A^c\)^c) is equal to what?
#sets
#complement
#double_complement
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A (A) / set (A)
B \(A^c\) / complement of (A)
C (U) / universal set
D \(\varnothing\) / empty set
Explanation opens after your attempt
Correct Answer
A. (A) / set (A)
Step 1
Concept
The complement of the complement is the original set. So remember (\(A^c\)^c=A).
Step 2
Why this answer is correct
The correct answer is A. (A) / set (A). The complement of the complement is the original set. So remember (\(A^c\)^c=A).
Step 3
Exam Tip
पूरक का पूरक मूल समुच्चय होता है। इसलिए (\(A^c\)^c=A) याद रखें।
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यदि \(A\subseteq B\) है, तो पूरकों के लिए कौन सा संबंध सही है?
If \(A\subseteq B\), which relation is correct for the complements?
#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 complement of the larger set is smaller, so the order reverses. From \(A\subseteq B\), we get \(B^c\subseteq A^c\).
Step 2
Why this answer is correct
The correct answer is A. \(B^c\subseteq A^c\). The complement of the larger set is smaller, so the order reverses. From \(A\subseteq B\), we get \(B^c\subseteq A^c\).
Step 3
Exam Tip
बड़े समुच्चय का पूरक छोटा होता है, इसलिए क्रम उलट जाता है। \(A\subseteq B\) से \(B^c\subseteq A^c\) मिलता है।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\) और \(A=\{2,4,6,8,10\}\) है, तो \(A^c\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A=\{2,4,6,8,10\}\), what is \(A^c\)?
#sets
#complement
#odd_even
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A ({1,3,5,7,9})
B ({2,4,6,8,10})
C ({1,2,3,4,5})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,7,9})
Step 1
Concept
(A) contains the even numbers of (U), so the complement contains the odd numbers. In such questions, identify the pattern first.
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,7,9}). (A) contains the even numbers of (U), so the complement contains the odd numbers. In such questions, identify the pattern first.
Step 3
Exam Tip
(A) में (U) की सम संख्याएं हैं, इसलिए पूरक में विषम संख्याएं आएंगी। ऐसे प्रश्न में पहले पैटर्न पहचानें।
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\(यदि (U={\)अ,आ,इ,क,ख\(}) और (A={\)अ,आ,इ\(}) है, तो (A^c) क्या होगा\)?
\(If (U={\)a,e,i,k,m\(}) and (A={\)a,e,i\(}), what is (A^c)\)?
#sets
#complement
#letters
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A ({क,ख}) / ({k,m})
B ({अ,आ,इ}) / ({a,e,i})
C ({अ,क}) / ({a,k})
D (U)
Explanation opens after your attempt
Correct Answer
A. ({क,ख}) / ({k,m})
Step 1
Concept
\(A^c\) will contain the letters of (U) that are not in (A). In list questions, cross out and write the remaining elements.
Step 2
Why this answer is correct
The correct answer is A. ({क,ख}) / ({k,m\(}). (A^c) will contain the letters of (U) that are not in (A). In list questions, cross out and write the remaining elements.\)
Step 3
Exam Tip
\(A^c\) में (U) के वे अक्षर होंगे जो (A) में नहीं हैं। सूची वाले प्रश्नों में काटकर बचे तत्व लिखें।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\) और \(A=\{2,3,5,7\}\) है, तो \(A^c\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(A=\{2,3,5,7\}\), what is \(A^c\)?
#sets
#complement
#prime_numbers
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A ({1,4,6,8,9})
B ({2,3,5,7})
C ({4,6,8})
D ({1,9})
Explanation opens after your attempt
Correct Answer
A. ({1,4,6,8,9})
Step 1
Concept
(A) contains the given prime numbers, so the remaining elements are in \(A^c\). Do not treat (1) as a prime number.
Step 2
Why this answer is correct
The correct answer is A. ({1,4,6,8,9}). (A) contains the given prime numbers, so the remaining elements are in \(A^c\). Do not treat (1) as a prime number.
Step 3
Exam Tip
(A) में दी हुई अभाज्य संख्याएं हैं, इसलिए बाकी तत्व \(A^c\) में हैं। (1) को अभाज्य न मानें।
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डी मॉर्गन नियम के अनुसार (\(A\cup B\)^c) किसके बराबर होता है?
According to De Morgan's law, (\(A\cup B\)^c) is equal to what?
#sets
#complement
#de_morgan_union
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A \(A^c\cap B^c\)
B \(A^c\cup B^c\)
C \(A\cap B\)
D \(A\cup B\)
Explanation opens after your attempt
Correct Answer
A. \(A^c\cap B^c\)
Step 1
Concept
(\(A\cup B\)^c) contains elements outside both sets. Therefore it equals \(A^c\cap B^c\).
Step 2
Why this answer is correct
The correct answer is A. \(A^c\cap B^c\). (\(A\cup B\)^c) contains elements outside both sets. Therefore it equals \(A^c\cap B^c\).
Step 3
Exam Tip
(\(A\cup B\)^c) में दोनों समुच्चयों से बाहर के तत्व आते हैं। इसलिए यह \(A^c\cap B^c\) के बराबर है।
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डी मॉर्गन नियम के अनुसार (\(A\cap B\)^c) किसके बराबर होता है?
According to De Morgan's law, (\(A\cap B\)^c) is equal to what?
#sets
#complement
#de_morgan_intersection
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A \(A^c\cup B^c\)
B \(A^c\cap B^c\)
C \(A\cup B\)
D \(A\cap B\)
Explanation opens after your attempt
Correct Answer
A. \(A^c\cup B^c\)
Step 1
Concept
(\(A\cap B\)^c) means the part outside the common part. By De Morgan's law, it is \(A^c\cup B^c\).
Step 2
Why this answer is correct
The correct answer is A. \(A^c\cup B^c\). (\(A\cap B\)^c) means the part outside the common part. By De Morgan's law, it is \(A^c\cup B^c\).
Step 3
Exam Tip
(\(A\cap B\)^c) का अर्थ है साझा भाग के बाहर का भाग। डी मॉर्गन नियम से यह \(A^c\cup B^c\) होता है।
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यदि \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\) और \(B=\{3,4\}\) है, तो (\(A\cup B\)^c) क्या होगा?
If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), and \(B=\{3,4\}\), what is (\(A\cup B\)^c)?
#sets
#complement
#union_application
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A ({5,6})
B ({1,2,3,4})
C ({3})
D ({1,2,5,6})
Explanation opens after your attempt
Correct Answer
A. ({5,6})
Step 1
Concept
First \(A\cup B={1,2,3,4}\). Its complement is the remaining elements (5) and (6) in (U).
Step 2
Why this answer is correct
The correct answer is A. ({5,6}). First \(A\cup B={1,2,3,4}\). Its complement is the remaining elements (5) and (6) in (U).
Step 3
Exam Tip
पहले \(A\cup B={1,2,3,4}\) बनता है। इसका पूरक (U) में बचे (5) और (6) हैं।
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यदि \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\) और \(B=\{3,4\}\) है, तो (\(A\cap B\)^c) क्या होगा?
If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), and \(B=\{3,4\}\), what is (\(A\cap B\)^c)?
#sets
#complement
#intersection_application
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A ({1,2,4,5,6})
B ({3})
C ({1,2,3,4})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,2,4,5,6})
Step 1
Concept
Here \(A\cap B={3}\). Removing (3) from (U) gives ({1,2,4,5,6}).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,4,5,6}). Here \(A\cap B={3}\). Removing (3) from (U) gives ({1,2,4,5,6}).
Step 3
Exam Tip
यहां \(A\cap B={3}\) है। इसलिए (U) से (3) हटाने पर ({1,2,4,5,6}) मिलता है।
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यदि \(U=\{0,1,2,3,4\}\) और \(A=\{0,2,4\}\) है, तो \(A^c\) ज्ञात करें।
If \(U=\{0,1,2,3,4\}\) and \(A=\{0,2,4\}\), find \(A^c\).
#sets
#complement
#zero_in_set
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A ({1,3})
B ({0,2,4})
C ({0,1,3})
D ({2,4})
Explanation opens after your attempt
Correct Answer
A. ({1,3})
Step 1
Concept
(A) has (0), (2), and (4), so the remaining elements (1) and (3) are the complement. Count (0) as an element too.
Step 2
Why this answer is correct
The correct answer is A. ({1,3}). (A) has (0), (2), and (4), so the remaining elements (1) and (3) are the complement. Count (0) as an element too.
Step 3
Exam Tip
(A) में (0), (2) और (4) हैं, इसलिए (U) में बचे (1) और (3) पूरक हैं। (0) को भी तत्व की तरह गिनें।
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यदि \(U=\{1,2,3,4\}\) और \(A=\{1,4\}\) है, तो कौन सा कथन सही है?
If \(U=\{1,2,3,4\}\) and \(A=\{1,4\}\), which statement is correct?
#sets
#complement
#true_statement
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A \(2\in A^c\)
B \(1\in A^c\)
C \(4\notin A\)
D \(3\in A\)
Explanation opens after your attempt
Correct Answer
A. \(2\in A^c\)
Step 1
Concept
\(A^c={2,3}\), so \(2\in A^c\) is correct. For membership, write the complement clearly first.
Step 2
Why this answer is correct
The correct answer is A. \(2\in A^c\). \(A^c={2,3}\), so \(2\in A^c\) is correct. For membership, write the complement clearly first.
Step 3
Exam Tip
\(A^c={2,3}\), इसलिए \(2\in A^c\) सही है। सदस्यता में पहले पूरक स्पष्ट लिखें।
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कौन सा कथन हर समुच्चय (A) के लिए हमेशा सही है?
Which statement is always true for every set (A)?
#sets
#complement
#always_true
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A \(A^c\subseteq U\)
B \(U\subseteq A^c\)
C \(A^c=A\)
D \(A^c=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(A^c\subseteq U\)
Step 1
Concept
\(A^c\) is always inside (U). Therefore \(A^c\subseteq U\) is always true.
Step 2
Why this answer is correct
The correct answer is A. \(A^c\subseteq U\). \(A^c\) is always inside (U). Therefore \(A^c\subseteq U\) is always true.
Step 3
Exam Tip
\(A^c\) हमेशा (U) के अंदर ही होता है। इसलिए \(A^c\subseteq U\) हर बार सही है।
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यदि \(A^c=\varnothing\) है, तो (A) किसके बराबर होगा?
If \(A^c=\varnothing\), then (A) is equal to what?
#sets
#complement
#empty_complement
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A (U) / universal set
B \(\varnothing\) / empty set
C \(A^c\) / complement of (A)
D \(U^c\) / complement of (U)
Explanation opens after your attempt
Correct Answer
A. (U) / universal set
Step 1
Concept
An empty complement means no element of (U) is outside (A). Therefore (A=U).
Step 2
Why this answer is correct
The correct answer is A. (U) / universal set. An empty complement means no element of (U) is outside (A). Therefore (A=U).
Step 3
Exam Tip
पूरक खाली होने का अर्थ है कि (U) का कोई तत्व (A) से बाहर नहीं है। इसलिए (A=U) होगा।
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यदि \(A^c=U\) है, तो (A) किसके बराबर होगा?
If \(A^c=U\), then (A) is equal to what?
#sets
#complement
#universal_complement
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A \(\varnothing\) / empty set
B (U) / universal set
C \(A^c\) / complement of (A)
D \(U-\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\) / empty set
Step 1
Concept
If the whole (U) is outside (A), then (A) has no element. Therefore \(A=\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\) / empty set. If the whole (U) is outside (A), then (A) has no element. Therefore \(A=\varnothing\).
Step 3
Exam Tip
यदि पूरा (U) ही (A) के बाहर है, तो (A) में कोई तत्व नहीं है। इसलिए \(A=\varnothing\) होगा।
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वेन आरेख में आयत (U) है और वृत्त (A) है। वृत्त के बाहर लेकिन आयत के अंदर का भाग क्या कहलाता है?
In a Venn diagram, the rectangle is (U) and the circle is (A). What is the part outside the circle but inside the rectangle called?
#sets
#complement
#venn_diagram
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A \(A^c\) / complement of (A)
B (A) / set (A)
C \(U^c\) / complement of (U)
D \(A\cap U\)
Explanation opens after your attempt
Correct Answer
A. \(A^c\) / complement of (A)
Step 1
Concept
The part inside the rectangle and outside (A) is \(A^c\). In Venn diagrams, do not go outside the boundary of (U).
Step 2
Why this answer is correct
The correct answer is A. \(A^c\) / complement of (A). The part inside the rectangle and outside (A) is \(A^c\). In Venn diagrams, do not go outside the boundary of (U).
Step 3
Exam Tip
आयत के अंदर और (A) के बाहर वाला भाग \(A^c\) होता है। वेन आरेख में (U) की सीमा से बाहर न जाएं।
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\(यदि (U={x:x\) एक वर्ण है\(}) और (A={x:x\) एक स्वर है\(}) है, तो (A^c) क्या दर्शाता है\)?
\(If (U={x:x\) is an alphabet letter\(}) and (A={x:x\) is a vowel\(}), what does (A^c) represent\)?
#sets
#complement
#set_builder
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A ({x:x एक व्यंजन है}) / ({x:x is a consonant})
B ({x:x एक स्वर है}) / ({x:x is a vowel})
C \(\varnothing\) / empty set
D (U) / universal set
Explanation opens after your attempt
Correct Answer
A. ({x:x एक व्यंजन है}) / ({x:x is a consonant})
Step 1
Concept
Removing vowels from (U) leaves consonants. Always understand complement with respect to the given (U).
Step 2
Why this answer is correct
The correct answer is A. ({x:x एक व्यंजन है}) / ({x:x is a consonant}). Removing vowels from (U) leaves consonants. Always understand complement with respect to the given (U).
Step 3
Exam Tip
स्वरों को (U) से हटाने पर व्यंजन बचते हैं। पूरक हमेशा दिए गए (U) के संदर्भ में समझें।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10,11,12\}\) और \(A=\{3,6,9,12\}\) है, तो \(A^c\) क्या होगा?
If \(U=\{1,2,3,4,5,6,7,8,9,10,11,12\}\) and \(A=\{3,6,9,12\}\), what is \(A^c\)?
#sets
#complement
#multiples
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A ({1,2,4,5,7,8,10,11})
B ({3,6,9,12})
C ({1,3,5,7,9,11})
D ({2,4,6,8,10,12})
Explanation opens after your attempt
Correct Answer
A. ({1,2,4,5,7,8,10,11})
Step 1
Concept
(A) contains multiples of (3), so the remaining elements of (U) form \(A^c\). For speed, cross out (A) from (U).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,4,5,7,8,10,11}). (A) contains multiples of (3), so the remaining elements of (U) form \(A^c\). For speed, cross out (A) from (U).
Step 3
Exam Tip
(A) में (3) के गुणज हैं, इसलिए (U) में बचे हुए तत्व \(A^c\) हैं। जल्दी करने के लिए (U) से (A) को काटें।
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यदि (n(U)=30) और (n\(A^c\)=18) है, तो (n(A)) कितना होगा?
If (n(U)=30) and (n\(A^c\)=18), what is (n(A))?
#sets
#complement
#count_reverse
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A (12)
B (48)
C (18)
D (30)
Explanation opens after your attempt
Step 1
Concept
(n(A)=n(U)-n\(A^c\)). Therefore (30-18=12) is correct.
Step 2
Why this answer is correct
The correct answer is A. (12). (n(A)=n(U)-n\(A^c\)). Therefore (30-18=12) is correct.
Step 3
Exam Tip
(n(A)=n(U)-n\(A^c\)) होता है। इसलिए (30-18=12) सही है।
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यदि (n(U)=16) और (n(A)=n\(A^c\)) है, तो (n(A)) कितना होगा?
If (n(U)=16) and (n(A)=n\(A^c\)), what is (n(A))?
#sets
#complement
#equal_cardinality
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A (8)
B (16)
C (4)
D (0)
Explanation opens after your attempt
Step 1
Concept
(A) and \(A^c\) together form (U), and their counts are equal. Hence \(16\div 2=8\).
Step 2
Why this answer is correct
The correct answer is A. (8). (A) and \(A^c\) together form (U), and their counts are equal. Hence \(16\div 2=8\).
Step 3
Exam Tip
(A) और \(A^c\) मिलकर (U) बनाते हैं और दोनों की संख्या बराबर है। इसलिए \(16\div 2=8\) होगा।
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कौन से दो समुच्चय हमेशा असंबद्ध होते हैं?
Which two sets are always disjoint?
#sets
#complement
#disjoint_sets
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A (A) और \(A^c\) / (A) and \(A^c\)
B (A) और (U) / (A) and (U)
C \(A^c\) और (U) / \(A^c\) and (U)
D (U) और (U) / (U) and (U)
Explanation opens after your attempt
Correct Answer
A. (A) और \(A^c\) / (A) and \(A^c\)
Step 1
Concept
\(A\cap A^c=\varnothing\), so (A) and \(A^c\) are always disjoint. This property is clear in a Venn diagram.
Step 2
Why this answer is correct
The correct answer is A. (A) और \(A^c\) / (A) and \(A^c\). \(A\cap A^c=\varnothing\), so (A) and \(A^c\) are always disjoint. This property is clear in a Venn diagram.
Step 3
Exam Tip
\(A\cap A^c=\varnothing\), इसलिए (A) और \(A^c\) हमेशा असंबद्ध होते हैं। यह गुण वेन आरेख में तुरंत दिखता है।
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यदि (n(U)=25) है, तो (n\(A\cup A^c\)) कितना होगा?
If (n(U)=25), what is (n\(A\cup A^c\))?
#sets
#complement
#cardinality_union
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A (25)
B (0)
C (n(A))
D (n\(A^c\))
Explanation opens after your attempt
Step 1
Concept
\(A\cup A^c=U\). Therefore (n\(A\cup A^c\)=n(U)=25).
Step 2
Why this answer is correct
The correct answer is A. (25). \(A\cup A^c=U\). Therefore (n\(A\cup A^c\)=n(U)=25).
Step 3
Exam Tip
\(A\cup A^c=U\) होता है। इसलिए (n\(A\cup A^c\)=n(U)=25) होगा।
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किसी भी समुच्चय (A) के लिए (n\(A\cap A^c\)) कितना होता है?
For any set (A), what is (n\(A\cap A^c\))?
#sets
#complement
#cardinality_intersection
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A (0)
B (1)
C (n(U))
D (n(A))
Explanation opens after your attempt
Step 1
Concept
\(A\cap A^c=\varnothing\), so it has no element. Hence its cardinality is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). \(A\cap A^c=\varnothing\), so it has no element. Hence its cardinality is (0).
Step 3
Exam Tip
\(A\cap A^c=\varnothing\), इसलिए इसमें कोई तत्व नहीं होता। अतः इसकी संख्या (0) है।
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(U-A) किसके बराबर होता है?
What is (U-A) equal to?
#sets
#complement
#set_difference
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A \(A^c\) / complement of (A)
B (A) / set (A)
C (U) / universal set
D \(\varnothing\) / empty set
Explanation opens after your attempt
Correct Answer
A. \(A^c\) / complement of (A)
Step 1
Concept
(U-A) means removing the elements of (A) from (U). This is the definition of \(A^c\).
Step 2
Why this answer is correct
The correct answer is A. \(A^c\) / complement of (A). (U-A) means removing the elements of (A) from (U). This is the definition of \(A^c\).
Step 3
Exam Tip
(U-A) का अर्थ (U) में से (A) के तत्व हटाना है। यही \(A^c\) की परिभाषा है।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(A=\{1,2,3,4\}\) है, तो (U-A) क्या होगा?
If \(U=\{1,2,3,4,5,6\}\) and \(A=\{1,2,3,4\}\), what is (U-A)?
#sets
#complement
#difference_example
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A ({5,6})
B ({1,2,3,4})
C ({1,2})
D (U)
Explanation opens after your attempt
Correct Answer
A. ({5,6})
Step 1
Concept
\(U-A=A^c\), so after removing the elements of (A), (5) and (6) remain. Link difference and complement with respect to (U).
Step 2
Why this answer is correct
The correct answer is A. ({5,6}). \(U-A=A^c\), so after removing the elements of (A), (5) and (6) remain. Link difference and complement with respect to (U).
Step 3
Exam Tip
\(U-A=A^c\) होता है, इसलिए (A) के तत्व हटाने पर (5) और (6) बचते हैं। अंतर और पूरक को (U) के संदर्भ में जोड़कर देखें।
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यदि \(U=\{1,2,3,4,5,6,7\}\) और \(A=\{2,3,5,7\}\) है, तो \(A^c\) कौन सा है?
If \(U=\{1,2,3,4,5,6,7\}\) and \(A=\{2,3,5,7\}\), which is \(A^c\)?
#sets
#complement
#prime_set
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A ({1,4,6})
B ({2,3,5,7})
C ({1,2,4,6})
D ({3,5,7})
Explanation opens after your attempt
Correct Answer
A. ({1,4,6})
Step 1
Concept
(A) has (2), (3), (5), (7), so (1), (4), (6) are the complement. Do not add any number outside the given (U).
Step 2
Why this answer is correct
The correct answer is A. ({1,4,6}). (A) has (2), (3), (5), (7), so (1), (4), (6) are the complement. Do not add any number outside the given (U).
Step 3
Exam Tip
(A) में (2), (3), (5), (7) हैं, इसलिए बाकी (1), (4), (6) पूरक हैं। दिए हुए (U) से बाहर कोई संख्या न जोड़ें।
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\(यदि (U={\)सोमवार,मंगलवार,बुधवार,गुरुवार,शुक्रवार,शनिवार,रविवार\(}) और (A={\)शनिवार,रविवार\(}) है, तो (A^c) क्या दर्शाता है\)?
\(If (U={\)Monday,Tuesday,Wednesday,Thursday,Friday,Saturday,Sunday\(}) and (A={\)Saturday,Sunday\(}), what does (A^c) represent\)?
#sets
#complement
#real_life
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A ({सोमवार,मंगलवार,बुधवार,गुरुवार,शुक्रवार}) / weekdays
B ({शनिवार,रविवार}) / weekend days
C (U) / all days
D \(\varnothing\) / no day
Explanation opens after your attempt
Correct Answer
A. ({सोमवार,मंगलवार,बुधवार,गुरुवार,शुक्रवार}) / weekdays
Step 1
Concept
(A) contains weekend days, so \(A^c\) contains weekdays. The same complement rule applies to word sets also.
Step 2
Why this answer is correct
The correct answer is A. ({सोमवार,मंगलवार,बुधवार,गुरुवार,शुक्रवार\(}) / weekdays. (A) contains weekend days, so (A^c) contains weekdays. The same complement rule applies to word sets also.\)
Step 3
Exam Tip
(A) में सप्ताहांत के दिन हैं, इसलिए \(A^c\) में कार्यदिवस होंगे। शब्दों वाले समुच्चय में भी वही पूरक नियम लगता है।
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इनमें से कौन सा कथन गलत है?
Which of the following statements is false?
#sets
#complement
#false_statement
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A \(A\cap A^c=U\)
B \(A\cup A^c=U\)
C (\(A^c\)^c=A)
D \(A^c\subseteq U\)
Explanation opens after your attempt
Correct Answer
A. \(A\cap A^c=U\)
Step 1
Concept
\(A\cap A^c=\varnothing\), not (U). To identify a false statement, remember the basic properties.
Step 2
Why this answer is correct
The correct answer is A. \(A\cap A^c=U\). \(A\cap A^c=\varnothing\), not (U). To identify a false statement, remember the basic properties.
Step 3
Exam Tip
\(A\cap A^c=\varnothing\) होता है, (U) नहीं। गलत कथन पहचानने में मूल गुणों को याद रखें।
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यदि \(U=\{1,2,3,4,5\}\) और \(A^c={2,5}\) है, तो \(A\cap A^c\) क्या होगा?
If \(U=\{1,2,3,4,5\}\) and \(A^c={2,5}\), what is \(A\cap A^c\)?
#sets
#complement
#shortcut
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A \(\varnothing\) / empty set
B ({2,5})
C ({1,3,4})
D (U)
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\) / empty set
Step 1
Concept
For any (A), \(A\cap A^c=\varnothing\). Here there is no need to find (A) first.
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\) / empty set. For any (A), \(A\cap A^c=\varnothing\). Here there is no need to find (A) first.
Step 3
Exam Tip
किसी भी (A) के लिए \(A\cap A^c=\varnothing\) होता है। यहां (A) निकालने की भी जरूरत नहीं है।
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यदि \(U=\{1,2,3,4,5\}\) और \(A^c={2,5}\) है, तो \(A\cup A^c\) क्या होगा?
If \(U=\{1,2,3,4,5\}\) and \(A^c={2,5}\), what is \(A\cup A^c\)?
#sets
#complement
#union_shortcut
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A (U)
B ({2,5})
C \(\varnothing\)
D ({1,3,4})
Explanation opens after your attempt
Step 1
Concept
\(A\cup A^c\) is always (U). Therefore the answer is directly (U).
Step 2
Why this answer is correct
The correct answer is A. (U). \(A\cup A^c\) is always (U). Therefore the answer is directly (U).
Step 3
Exam Tip
\(A\cup A^c\) हमेशा (U) होता है। इसलिए उत्तर सीधे (U) है।
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यदि \(3\in U\) और \(3\notin A\) है, तो कौन सा निष्कर्ष सही है?
If \(3\in U\) and \(3\notin A\), which conclusion is correct?
#sets
#complement
#element_logic
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A \(3\in A^c\)
B \(3\in A\)
C \(3\notin U\)
D \(3\in A\cap A^c\)
Explanation opens after your attempt
Correct Answer
A. \(3\in A^c\)
Step 1
Concept
An element in (U) but not in (A) belongs to \(A^c\). This is the basic membership condition of complement.
Step 2
Why this answer is correct
The correct answer is A. \(3\in A^c\). An element in (U) but not in (A) belongs to \(A^c\). This is the basic membership condition of complement.
Step 3
Exam Tip
जो तत्व (U) में है और (A) में नहीं है, वह \(A^c\) में होगा। यह पूरक की मूल सदस्यता शर्त है।
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यदि \(4\in A^c\) है, तो कौन सा कथन सही है?
If \(4\in A^c\), which statement is correct?
#sets
#complement
#condition
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A \(4\in U\) और \(4\notin A\) / \(4\in U\) and \(4\notin A\)
B \(4\in A\) और \(4\in U\) / \(4\in A\) and \(4\in U\)
C \(4\notin U\)
D \(4\in A\cap A^c\)
Explanation opens after your attempt
Correct Answer
A. \(4\in U\) और \(4\notin A\) / \(4\in U\) and \(4\notin A\)
Step 1
Concept
An element of \(A^c\) is always in (U) and not in (A). In such questions, write both conditions together.
Step 2
Why this answer is correct
The correct answer is A. \(4\in U\) और \(4\notin A\) / \(4\in U\) and \(4\notin A\). An element of \(A^c\) is always in (U) and not in (A). In such questions, write both conditions together.
Step 3
Exam Tip
\(A^c\) का तत्व हमेशा (U) में होता है और (A) में नहीं होता। ऐसे प्रश्नों में दोनों शर्तें साथ लिखें।
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यदि \(U={x:x\in\mathbb{N},1\le x\le 5}\) और \(A=\{x:x<4\}\) है, तो \(A^c\) क्या होगा?
If \(U={x:x\in\mathbb{N},1\le x\le 5}\) and \(A=\{x:x<4\}\), what is \(A^c\)?
#sets
#complement
#set_builder_natural
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A ({4,5})
B ({1,2,3})
C ({1,2,3,4})
D ({5})
Explanation opens after your attempt
Correct Answer
A. ({4,5})
Step 1
Concept
\(U=\{1,2,3,4,5\}\) and \(A=\{1,2,3\}\). Therefore the remaining elements are (4) and (5).
Step 2
Why this answer is correct
The correct answer is A. ({4,5}). \(U=\{1,2,3,4,5\}\) and \(A=\{1,2,3\}\). Therefore the remaining elements are (4) and (5).
Step 3
Exam Tip
\(U=\{1,2,3,4,5\}\) और \(A=\{1,2,3\}\) है। इसलिए बचे हुए तत्व (4) और (5) हैं।
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यदि \(U={x:x\in\mathbb{N},x\le 8}\) और \(A=\{1,3,5,7\}\) है, तो \(A^c\) क्या होगा?
If \(U={x:x\in\mathbb{N},x\le 8}\) and \(A=\{1,3,5,7\}\), what is \(A^c\)?
#sets
#complement
#odd_even_builder
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A ({2,4,6,8})
B ({1,3,5,7})
C ({1,2,3,4})
D ({5,6,7,8})
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Correct Answer
A. ({2,4,6,8})
Step 1
Concept
\(U=\{1,2,3,4,5,6,7,8\}\), and (A) has odd numbers. The complement contains even numbers.
Step 2
Why this answer is correct
The correct answer is A. ({2,4,6,8}). \(U=\{1,2,3,4,5,6,7,8\}\), and (A) has odd numbers. The complement contains even numbers.
Step 3
Exam Tip
\(U=\{1,2,3,4,5,6,7,8\}\) है और (A) में विषम संख्याएं हैं। पूरक में सम संख्याएं आएंगी।
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यदि (U=[0,10]) और (A=[0,4]) है, तो \(A^c\) क्या होगा?
If (U=[0,10]) and (A=[0,4]), what is \(A^c\)?
#sets
#complement
#intervals
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A ((4,10])
B ([4,10])
C ([0,4])
D ([0,10])
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Correct Answer
A. ((4,10])
Step 1
Concept
(4) is included in (A), so the complement starts after (4). Since (10) is included in (U), ((4,10]) is correct.
Step 2
Why this answer is correct
The correct answer is A. ((4,10]). (4) is included in (A), so the complement starts after (4). Since (10) is included in (U), ((4,10]) is correct.
Step 3
Exam Tip
(A) में (4) शामिल है, इसलिए पूरक (4) के बाद से शुरू होगा। (10) (U) में शामिल है, इसलिए ((4,10]) सही है।
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यदि (U=[-2,3]) और (A=(-1,2]) है, तो \(A^c\) क्या होगा?
If (U=[-2,3]) and (A=(-1,2]), what is \(A^c\)?
#sets
#complement
#interval_complement
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A ([-2,-1]\cup(2,3])
B ((-1,2])
C ([-2,3])
D ([-1,2])
Explanation opens after your attempt
Correct Answer
A. ([-2,-1]\cup(2,3])
Step 1
Concept
(-1) is not included in (A), so (-1) is in the complement. (2) is in (A), so the complement starts after (2).
Step 2
Why this answer is correct
The correct answer is A. ([-2,-1]\cup(2,3]). (-1) is not included in (A), so (-1) is in the complement. (2) is in (A), so the complement starts after (2).
Step 3
Exam Tip
(A) में (-1) शामिल नहीं है, इसलिए (-1) पूरक में आएगा। (2) (A) में है, इसलिए पूरक (2) के बाद शुरू होगा।
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किसी कक्षा में (U) सभी विद्यार्थी हैं और (A) क्रिकेट खेलने वाले विद्यार्थी हैं। \(A^c\) क्या दर्शाता है?
In a class, (U) is the set of all students and (A) is the set of students who play cricket. What does \(A^c\) represent?
#sets
#complement
#application
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A क्रिकेट न खेलने वाले विद्यार्थी / students who do not play cricket
B क्रिकेट खेलने वाले विद्यार्थी / students who play cricket
C सभी विद्यार्थी / all students
D कोई विद्यार्थी नहीं / no student
Explanation opens after your attempt
Correct Answer
A. क्रिकेट न खेलने वाले विद्यार्थी / students who do not play cricket
Step 1
Concept
\(A^c\) contains the students of (U) who are not in (A). So it is the set of students who do not play cricket.
Step 2
Why this answer is correct
The correct answer is A. क्रिकेट न खेलने वाले विद्यार्थी / students who do not play cricket. \(A^c\) contains the students of (U) who are not in (A). So it is the set of students who do not play cricket.
Step 3
Exam Tip
\(A^c\) में (U) के वे विद्यार्थी होंगे जो (A) में नहीं हैं। इसलिए यह क्रिकेट न खेलने वालों का समुच्चय है।
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एक सर्वे में (n(U)=40) और (n\(A^c\)=15) है। (n(A)) कितना होगा?
In a survey, (n(U)=40) and (n\(A^c\)=15). What is (n(A))?
#sets
#complement
#survey
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A (25)
B (55)
C (15)
D (40)
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Step 1
Concept
(n(A)=n(U)-n\(A^c\)). Therefore (40-15=25).
Step 2
Why this answer is correct
The correct answer is A. (25). (n(A)=n(U)-n\(A^c\)). Therefore (40-15=25).
Step 3
Exam Tip
(n(A)=n(U)-n\(A^c\)) होता है। इसलिए (40-15=25) मिलेगा।
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यदि (A) सार्वत्रिक समुच्चय (U) का वास्तविक उपसमुच्चय है, तो \(A^c\) के बारे में क्या सही है?
If (A) is a proper subset of the universal set (U), what is true about \(A^c\)?
#sets
#complement
#proper_subset
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A \(A^c\ne\varnothing\)
B \(A^c=\varnothing\)
C \(A^c=A\)
D \(A^c\not\subseteq U\)
Explanation opens after your attempt
Correct Answer
A. \(A^c\ne\varnothing\)
Step 1
Concept
If (A) is a proper subset, at least one element of (U) is outside (A). Therefore \(A^c\ne\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(A^c\ne\varnothing\). If (A) is a proper subset, at least one element of (U) is outside (A). Therefore \(A^c\ne\varnothing\).
Step 3
Exam Tip
वास्तविक उपसमुच्चय होने पर (U) में कम से कम एक तत्व (A) से बाहर होगा। इसलिए \(A^c\ne\varnothing\) है।
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यदि \(A=\{1,2\}\), \(U_1={1,2,3}\) और \(U_2={1,2,3,4}\) हैं, तो (A) का पूरक दोनों में अलग क्यों होगा?
If \(A=\{1,2\}\), \(U_1={1,2,3}\), and \(U_2={1,2,3,4}\), why will the complement of (A) be different in both cases?
#sets
#complement
#universal_dependency
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A क्योंकि सार्वत्रिक समुच्चय बदलता है / because the universal set changes
B क्योंकि (A) बदलता है / because (A) changes
C क्योंकि \(1\in A\) है / because \(1\in A\)
D क्योंकि \(2\in A\) है / because \(2\in A\)
Explanation opens after your attempt
Correct Answer
A. क्योंकि सार्वत्रिक समुच्चय बदलता है / because the universal set changes
Step 1
Concept
The complement always depends on the given universal set. When (U) changes, \(A^c\) may also change.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि सार्वत्रिक समुच्चय बदलता है / because the universal set changes. The complement always depends on the given universal set. When (U) changes, \(A^c\) may also change.
Step 3
Exam Tip
पूरक हमेशा दिए गए सार्वत्रिक समुच्चय पर निर्भर करता है। (U) बदलने पर \(A^c\) भी बदल सकता है।
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पूरक की जांच करने के लिए कौन सा युग्मित गुण सबसे उपयोगी है?
Which paired property is most useful to check a complement?
#sets
#complement
#property_check
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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 \(A^c=A\) और \(A\subseteq A^c\) / \(A^c=A\) and \(A\subseteq A^c\)
D \(U^c=U\) और \(\varnothing^c=\varnothing\) / \(U^c=U\) and \(\varnothing^c=\varnothing\)
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 correct complement, there should be no common element with (A), and both together should form (U). This is the best checking method in exams.
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 correct complement, there should be no common element with (A), and both together should form (U). This is the best checking method in exams.
Step 3
Exam Tip
सही पूरक के लिए (A) से कोई साझा तत्व नहीं होना चाहिए और दोनों मिलकर (U) बनने चाहिए। यही परीक्षा में सबसे अच्छा जांच तरीका है।
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