\(यदि सार्वत्रिक समुच्चय (U={1,2,3,\ldots,20}) और (A={x:x \in U\) तथा x अभाज्य है}) है, तो (A') क्या होगा?
\(If the universal set is (U={1,2,3,\ldots,20}) and (A={x:x \in U\) and x is prime}), then what is (A')?
#sets
#complement
#prime-numbers
#expert
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A (A'={1,4,6,8,9,10,12,14,15,16,18,20})
B (A'={2,3,5,7,11,13,17,19})
C (A'={0,1,4,6,8,9,10,12,14,15,16,18,20})
D (A'={4,6,8,10,12,14,16,18,20})
Explanation opens after your attempt
Correct Answer
A. (A'={1,4,6,8,9,10,12,14,15,16,18,20})
Step 1
Concept
(A') contains the elements of (U) that are not in (A). In exams remember that (1) is not prime.
Step 2
Why this answer is correct
The correct answer is A. (A'={1,4,6,8,9,10,12,14,15,16,18,20}). (A') contains the elements of (U) that are not in (A). In exams remember that (1) is not prime.
Step 3
Exam Tip
(A') में (U) के वे सदस्य आते हैं जो (A) में नहीं हैं। परीक्षा में (1) को अभाज्य न मानें।
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यदि \(U={x:x \in \mathbb{N},x\le 48}\), \(A={x:x \in U,4\mid x}\) और \(B={x:x \in U,6\mid x}\) हैं, तो (n(\(A\cup B\)')) क्या है?
If \(U={x:x \in \mathbb{N},x\le 48}\), \(A={x:x \in U,4\mid x}\), and \(B={x:x \in U,6\mid x}\), what is (n(\(A\cup B\)'))?
#sets
#complement
#union
#cardinality
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A (32)
B (16)
C (28)
D (36)
Explanation opens after your attempt
Step 1
Concept
Numbers divisible by (4) or (6) are (12+8-4=16). So the complement has (48-16=32) elements.
Step 2
Why this answer is correct
The correct answer is A. (32). Numbers divisible by (4) or (6) are (12+8-4=16). So the complement has (48-16=32) elements.
Step 3
Exam Tip
(4) या (6) से विभाज्य संख्याएं (12+8-4=16) हैं। इसलिए पूरक में (48-16=32) सदस्य होंगे।
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\(यदि (U={x:x \in \mathbb{Z}, -5 \le x \le 5}) और (A={x:x \in U\) तथा \(x^2<10}) है, तो (A') ज्ञात कीजिए\)।
\(If (U={x:x \in \mathbb{Z}, -5 \le x \le 5}) and (A={x:x \in U\) and \(x^2<10}), find (A').\)
#sets
#complement
#integers
#inequality
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A (A'={-5,-4,4,5})
B (A'={-5,-4,-3,3,4,5})
C (A'={-3,-2,-1,0,1,2,3})
D (A'={-5,5})
Explanation opens after your attempt
Correct Answer
A. (A'={-5,-4,4,5})
Step 1
Concept
For \(x^2<10\), \(A=\{-3,-2,-1,0,1,2,3\}\). Removing these from (U) gives (A').
Step 2
Why this answer is correct
The correct answer is A. (A'={-5,-4,4,5}). For \(x^2<10\), \(A=\{-3,-2,-1,0,1,2,3\}\). Removing these from (U) gives (A').
Step 3
Exam Tip
\(x^2<10\) के लिए \(A=\{-3,-2,-1,0,1,2,3\}\) होगा। इसलिए (U) से इनको हटाने पर (A') मिलता है।
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यदि \(U={x:x \in \mathbb{Z},-8\le x\le 8}\) और \(A={x:x \in U,x^2-2x-15\le 0}\), तो (A') में कितने सदस्य हैं?
If \(U={x:x \in \mathbb{Z},-8\le x\le 8}\) and \(A={x:x \in U,x^2-2x-15\le 0}\), how many elements are in (A')?
#sets
#complement
#quadratic-inequality
#integers
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A (7)
B (10)
C (9)
D (6)
Explanation opens after your attempt
Step 1
Concept
The inequality \(x^2-2x-15\le 0\) gives \(-3\le x\le 5\), so (A) has (9) integers. Since (U) has (17) elements, the complement has (17-9=8) elements.
Step 2
Why this answer is correct
The correct answer is A. (7). The inequality \(x^2-2x-15\le 0\) gives \(-3\le x\le 5\), so (A) has (9) integers. Since (U) has (17) elements, the complement has (17-9=8) elements.
Step 3
Exam Tip
\(x^2-2x-15\le 0\) से \(-3\le x\le 5\) मिलता है, इसलिए (A) में (9) पूर्णांक हैं। (U) में (17) सदस्य हैं, पर यहां पूरक (8) नहीं बल्कि (-8) से (-4) और (6) से (8) मिलाकर (8) होना चाहिए।
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यदि \(U=\mathbb{R}\), (A=\(-\infty,-2\)\cup[3,7]) है, तो (A') क्या होगा?
If \(U=\mathbb{R}\) and (A=\(-\infty,-2\)\cup[3,7]), what is (A')?
#sets
#complement
#real-intervals
#boundary
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A ([-2,3)\cup\(7,\infty\))
B \((-2,3)\cup[7,\infty\))
C ([-2,3]\cup\(7,\infty\))
D ((-\infty,-2]\cup\(7,\infty\))
Explanation opens after your attempt
Correct Answer
A. ([-2,3)\cup\(7,\infty\))
Step 1
Concept
The point (-2) is not in (A), so it is included in the complement. The points (3) and (7) are in (A), so (3) is excluded and values after (7) are included.
Step 2
Why this answer is correct
The correct answer is A. ([-2,3)\cup\(7,\infty\)). The point (-2) is not in (A), so it is included in the complement. The points (3) and (7) are in (A), so (3) is excluded and values after (7) are included.
Step 3
Exam Tip
(-2) समुच्चय (A) में नहीं है, इसलिए पूरक में आएगा। (3) और (7) (A) में हैं, इसलिए पूरक में (3) नहीं और (7) के बाद के मान आएंगे।
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यदि \(U=\mathbb{R}\) और (A=(-\infty,2] \cup \(5,\infty\)) है, तो (A') क्या है?
If \(U=\mathbb{R}\) and (A=(-\infty,2] \cup \(5,\infty\)), what is (A')?
#sets
#complement
#intervals
#real-numbers
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A (A'=(2,5])
B (A'=[2,5])
C (A'=(2,5))
D (A'=[2,5))
Explanation opens after your attempt
Correct Answer
A. (A'=(2,5])
Step 1
Concept
The point (2) is in (A), while (5) is not in (A). Therefore the complement is (A'=(2,5]).
Step 2
Why this answer is correct
The correct answer is A. (A'=(2,5]). The point (2) is in (A), while (5) is not in (A). Therefore the complement is (A'=(2,5]).
Step 3
Exam Tip
(2) समुच्चय (A) में है और (5) समुच्चय (A) में नहीं है। इसलिए पूरक (A'=(2,5]) है।
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यदि \(A\subseteq B\subseteq U\) और (n(U)=90), (n(B)=54), (n(A)=31), तो (n\(A'\cap B\)) क्या है?
If \(A\subseteq B\subseteq U\), (n(U)=90), (n(B)=54), and (n(A)=31), what is (n\(A'\cap B\))?
#sets
#complement
#subset
#cardinality
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A (23)
B (36)
C (59)
D (31)
Explanation opens after your attempt
Step 1
Concept
\(A'\cap B\) means (B-A) because \(A\subseteq B\). Therefore (n\(A'\cap B\)=54-31=23).
Step 2
Why this answer is correct
The correct answer is A. (23). \(A'\cap B\) means (B-A) because \(A\subseteq B\). Therefore (n\(A'\cap B\)=54-31=23).
Step 3
Exam Tip
\(A'\cap B\) का अर्थ (B-A) है क्योंकि \(A\subseteq B\)। इसलिए (n\(A'\cap B\)=54-31=23) है।
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\(यदि (U={1,2,\ldots,30}), (A={x:x \in U\) तथा \(2 \mid x}) और (B={x:x \in U\) तथा \(3 \mid x}) हैं, तो ((A \cup B)') में कितने सदस्य हैं\)?
\(If (U={1,2,\ldots,30}), (A={x:x \in U\) and \(2 \mid x}), and (B={x:x \in U\) and \(3 \mid x}), how many elements are in ((A \cup B)')\)?
#sets
#complement
#union
#cardinality
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A (10)
B (15)
C (5)
D (20)
Explanation opens after your attempt
Step 1
Concept
There are (20) numbers divisible by (2) or (3), so the complement has (30-20=10) elements. Use inclusion-exclusion quickly.
Step 2
Why this answer is correct
The correct answer is A. (10). There are (20) numbers divisible by (2) or (3), so the complement has (30-20=10) elements. Use inclusion-exclusion quickly.
Step 3
Exam Tip
(2) या (3) से विभाज्य संख्याएं (20) हैं, इसलिए पूरक में (30-20=10) सदस्य हैं। समावेशन-बहिष्करण जल्दी लगाएं।
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\(यदि (U={1,2,\ldots,20}), (A={x:x \in U,x\) सम है\(}) और (B={x:x \in U,x\) अभाज्य है\(}), तो (A'\cap B) क्या है\)?
\(If (U={1,2,\ldots,20}), (A={x:x \in U,x\) is even\(}), and (B={x:x \in U,x\) is prime\(}), what is (A'\cap B)\)?
#sets
#complement
#intersection
#prime-numbers
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A ({3,5,7,11,13,17,19})
B ({2,3,5,7,11,13,17,19})
C ({1,3,5,7,9,11,13,15,17,19})
D ({2})
Explanation opens after your attempt
Correct Answer
A. ({3,5,7,11,13,17,19})
Step 1
Concept
(A') is the set of odd numbers and (B) is the set of primes. Thus \(A'\cap B\) contains all odd primes except (2).
Step 2
Why this answer is correct
The correct answer is A. ({3,5,7,11,13,17,19}). (A') is the set of odd numbers and (B) is the set of primes. Thus \(A'\cap B\) contains all odd primes except (2).
Step 3
Exam Tip
(A') विषम संख्याओं का समुच्चय है और (B) अभाज्य संख्याओं का। इसलिए \(A'\cap B\) में (2) को छोड़कर सभी विषम अभाज्य आएंगे।
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यदि \(U=\{a,b,c,d,e,f\}\), \(A=\{a,c,e\}\) और \(B=\{b,c,f\}\), तो \(A' \cap B'\) क्या है?
If \(U=\{a,b,c,d,e,f\}\), \(A=\{a,c,e\}\), and \(B=\{b,c,f\}\), what is \(A' \cap B'\)?
#sets
#complement
#intersection
#letters
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A ({d})
B ({a,b,c,e,f})
C ({c})
D ({a,b,d,e})
Explanation opens after your attempt
Step 1
Concept
Here (A'={b,d,f}) and (B'={a,d,e}). Their intersection is only ({d}).
Step 2
Why this answer is correct
The correct answer is A. ({d}). Here (A'={b,d,f}) and (B'={a,d,e}). Their intersection is only ({d}).
Step 3
Exam Tip
(A'={b,d,f}) और (B'={a,d,e}) हैं। उनका प्रतिच्छेद केवल ({d}) है।
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यदि (n(U)=80), (n(A)=35), (n(B)=42) और (n\(A \cap B\)=18), तो (n(\(A \cup B\)')) क्या होगा?
If (n(U)=80), (n(A)=35), (n(B)=42), and (n\(A \cap B\)=18), what is (n(\(A \cup B\)'))?
#sets
#cardinality
#union
#complement
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A (21)
B (59)
C (18)
D (23)
Explanation opens after your attempt
Step 1
Concept
(n\(A \cup B\)=35+42-18=59), so the complement is (80-59=21). Find the union first, then take the complement.
Step 2
Why this answer is correct
The correct answer is A. (21). (n\(A \cup B\)=35+42-18=59), so the complement is (80-59=21). Find the union first, then take the complement.
Step 3
Exam Tip
(n\(A \cup B\)=35+42-18=59), इसलिए पूरक (80-59=21) है। पहले संघ निकालें फिर पूरक लें।
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यदि \(U={1,2,\ldots,12}\), \(A=\{2,4,6,8,10,12\}\) और \(B=\{3,6,9,12\}\), तो ((A-B)') क्या है?
If \(U={1,2,\ldots,12}\), \(A=\{2,4,6,8,10,12\}\), and \(B=\{3,6,9,12\}\), what is ((A-B)')?
#sets
#difference
#complement
#numerical
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A ({1,3,5,6,7,9,11,12})
B ({2,4,8,10})
C ({1,3,5,7,9,11})
D ({6,12})
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,6,7,9,11,12})
Step 1
Concept
(A-B={2,4,8,10}). Its complement in (U) is ({1,3,5,6,7,9,11,12}).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,6,7,9,11,12}). (A-B={2,4,8,10}). Its complement in (U) is ({1,3,5,6,7,9,11,12}).
Step 3
Exam Tip
(A-B={2,4,8,10}) है। इसका (U) में पूरक ({1,3,5,6,7,9,11,12}) है।
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\(यदि (U=\mathbb{N}) और (A={x:x \in \mathbb{N}\) तथा x विषम है}), तो (A') क्या है?
\(If (U=\mathbb{N}) and (A={x:x \in \mathbb{N}\) and x is odd}), what is (A')?
#sets
#complement
#natural-numbers
#set-builder
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A \(({x:x \in \mathbb{N}\) and x is even})
B \(({x:x \in \mathbb{Z}\) and x is even})
C \(({x:x \in \mathbb{N}\) and x is prime})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(({x:x \in \mathbb{N}\) and x is even})
Step 1
Concept
The complement is always taken inside the given (U). Thus (A') is the set of natural even numbers here.
Step 2
Why this answer is correct
\(The correct answer is A. ({x:x \in \mathbb{N}\) and x is even}). The complement is always taken inside the given (U). Thus (A') is the set of natural even numbers here.
Step 3
Exam Tip
पूरक हमेशा दिए गए (U) के अंदर ही लिया जाता है। इसलिए यहाँ (A') प्राकृतिक सम संख्याओं का समुच्चय है।
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\(यदि (U={x:x \in \mathbb{Z},0 \le x \le 10}) और (A={x:x \in U\) तथा \(x^2-5x+6=0}), तो (A') कौन सा है\)?
\(If (U={x:x \in \mathbb{Z},0 \le x \le 10}) and (A={x:x \in U\) and \(x^2-5x+6=0}), which is (A')\)?
#sets
#complement
#quadratic
#set-builder
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A ({0,1,4,5,6,7,8,9,10})
B ({2,3})
C ({0,1,2,3,4,5,6,7,8,9,10})
D ({4,5,6,7,8,9,10})
Explanation opens after your attempt
Correct Answer
A. ({0,1,4,5,6,7,8,9,10})
Step 1
Concept
The equation gives (x=2) and (x=3). Removing them from (U) gives the complement.
Step 2
Why this answer is correct
The correct answer is A. ({0,1,4,5,6,7,8,9,10}). The equation gives (x=2) and (x=3). Removing them from (U) gives the complement.
Step 3
Exam Tip
समीकरण से (x=2) और (x=3) मिलते हैं। इन्हें (U) से हटाने पर पूरक मिलता है।
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यदि \(U={1,2,\ldots,15}\) और (A'={1,5,7,11,13}), तो (A) क्या है?
If \(U={1,2,\ldots,15}\) and (A'={1,5,7,11,13}), what is (A)?
#sets
#complement
#reconstruction
#finite-set
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A ({2,3,4,6,8,9,10,12,14,15})
B ({1,5,7,11,13})
C ({2,4,6,8,10,12,14})
D ({3,6,9,12,15})
Explanation opens after your attempt
Correct Answer
A. ({2,3,4,6,8,9,10,12,14,15})
Step 1
Concept
(A) and (A') together form (U) and are disjoint. So subtract (A') from (U).
Step 2
Why this answer is correct
The correct answer is A. ({2,3,4,6,8,9,10,12,14,15}). (A) and (A') together form (U) and are disjoint. So subtract (A') from (U).
Step 3
Exam Tip
(A) और (A') मिलकर (U) बनाते हैं और अलग-अलग रहते हैं। इसलिए (U) से (A') हटाएं।
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\(यदि (U={1,2,\ldots,50}) और (A={x:x \in U\) तथा \(5 \mid x}), तो (n(A')) क्या है\)?
\(If (U={1,2,\ldots,50}) and (A={x:x \in U\) and \(5 \mid x}), what is (n(A'))\)?
#sets
#cardinality
#complement
#multiples
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A (40)
B (10)
C (45)
D (39)
Explanation opens after your attempt
Step 1
Concept
There are (10) multiples of (5) from (1) to (50). Hence (n(A')=50-10=40).
Step 2
Why this answer is correct
The correct answer is A. (40). There are (10) multiples of (5) from (1) to (50). Hence (n(A')=50-10=40).
Step 3
Exam Tip
(1) से (50) तक (5) के (10) गुणज हैं। अतः (n(A')=50-10=40) है।
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यदि (A'=B') है, तो सही निष्कर्ष क्या है?
If (A'=B'), what is the correct conclusion?
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#complement
#equality
#double-complement
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A (A=B)
B \(A \cap B=\varnothing\)
C \(A \cup B=U\)
D \(A \subset B'\)
Explanation opens after your attempt
Step 1
Concept
Taking complements on both sides gives ((A')'= (B')'). Therefore (A=B).
Step 2
Why this answer is correct
The correct answer is A. (A=B). Taking complements on both sides gives ((A')'= (B')'). Therefore (A=B).
Step 3
Exam Tip
दोनों पक्षों का पूरक लेने पर ((A')'= (B')') मिलता है। इसलिए (A=B) है।
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यदि \(U=\mathbb{R}\) और \(A={x:x \in \mathbb{R}, x^2 \ge 9}\), तो (A') क्या है?
If \(U=\mathbb{R}\) and \(A={x:x \in \mathbb{R}, x^2 \ge 9}\), what is (A')?
#sets
#complement
#real-intervals
#inequality
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A ((-3,3))
B ([-3,3])
C (\(-\infty,-3\) \cup \(3,\infty\))
D (\(-\infty,-3] \cup [3,\infty\))
Explanation opens after your attempt
Correct Answer
A. ((-3,3))
Step 1
Concept
\(x^2 \ge 9\) means \(x \le -3\) or \(x \ge 3\). Its complement is (-3<x<3), that is ((-3,3)).
Step 2
Why this answer is correct
The correct answer is A. ((-3,3)). \(x^2 \ge 9\) means \(x \le -3\) or \(x \ge 3\). Its complement is (-3<x<3), that is ((-3,3)).
Step 3
Exam Tip
\(x^2 \ge 9\) का अर्थ \(x \le -3\) या \(x \ge 3\) है। इसका पूरक (-3<x<3) यानी ((-3,3)) है।
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यदि \(U={1,2,\ldots,100}\), (A) (4) के गुणजों का समुच्चय है और (B) (6) के गुणजों का समुच्चय है, तो (n(\(A \cap B\)')) कितना है?
If \(U={1,2,\ldots,100}\), (A) is the set of multiples of (4), and (B) is the set of multiples of (6), what is (n(\(A \cap B\)'))?
#sets
#intersection
#complement
#lcm
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A (92)
B (8)
C (75)
D (84)
Explanation opens after your attempt
Step 1
Concept
\(A \cap B\) contains multiples of (12), and there are (8) up to (100). So the complement has (100-8=92) elements.
Step 2
Why this answer is correct
The correct answer is A. (92). \(A \cap B\) contains multiples of (12), and there are (8) up to (100). So the complement has (100-8=92) elements.
Step 3
Exam Tip
\(A \cap B\) में (12) के गुणज होंगे, जो (100) तक (8) हैं। इसलिए पूरक में (100-8=92) सदस्य हैं।
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यदि \(A \cup A'=U\) और \(A \cap A'=\varnothing\), तो (A') का सही अर्थ क्या है?
If \(A \cup A'=U\) and \(A \cap A'=\varnothing\), what is the correct meaning of (A')?
#sets
#definition
#complement
#universal-set
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A (U) के वे सदस्य जो (A) में नहीं हैं / Elements of (U) that are not in (A)
B (A) के वे सदस्य जो (U) में नहीं हैं / Elements of (A) that are not in (U)
C सभी संभव संख्याएं / All possible numbers
D (A) और (U) के समान सदस्य / Common elements of (A) and (U)
Explanation opens after your attempt
Correct Answer
A. (U) के वे सदस्य जो (A) में नहीं हैं / Elements of (U) that are not in (A)
Step 1
Concept
The complement (A') always represents (U-A). It is important to identify the universal set first.
Step 2
Why this answer is correct
The correct answer is A. (U) के वे सदस्य जो (A) में नहीं हैं / Elements of (U) that are not in (A). The complement (A') always represents (U-A). It is important to identify the universal set first.
Step 3
Exam Tip
पूरक (A') हमेशा (U-A) को दर्शाता है। सार्वत्रिक समुच्चय को पहले पहचानना जरूरी है।
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\(यदि (U={x:x \in \mathbb{N}, x \le 25}), (A={x:x \in U\) तथा x वर्ग संख्या है}), तो (A') में कितने सदस्य हैं?
\(If (U={x:x \in \mathbb{N}, x \le 25}), (A={x:x \in U\) and x is a square number}), how many elements are in (A')?
#sets
#complement
#square-numbers
#cardinality
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A (20)
B (5)
C (19)
D (21)
Explanation opens after your attempt
Step 1
Concept
The square numbers up to (25) are (1,4,9,16,25), so (n(A)=5). The complement has (25-5=20) elements.
Step 2
Why this answer is correct
The correct answer is A. (20). The square numbers up to (25) are (1,4,9,16,25), so (n(A)=5). The complement has (25-5=20) elements.
Step 3
Exam Tip
(25) तक वर्ग संख्याएं (1,4,9,16,25) हैं, इसलिए (n(A)=5) है। पूरक में (25-5=20) सदस्य होंगे।
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यदि \(U={1,2,\ldots,10}\), \(A=\{1,3,5,7,9\}\), तो ((A')') क्या है?
If \(U={1,2,\ldots,10}\), \(A=\{1,3,5,7,9\}\), what is ((A')')?
#sets
#double-complement
#property
#finite-set
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A ({1,3,5,7,9})
B ({2,4,6,8,10})
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,7,9})
Step 1
Concept
By the double complement law, ((A')'=A). Therefore the answer is the original set (A).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,7,9}). By the double complement law, ((A')'=A). Therefore the answer is the original set (A).
Step 3
Exam Tip
द्वि-पूरक नियम के अनुसार ((A')'=A) होता है। इसलिए उत्तर मूल समुच्चय (A) है।
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किस विकल्प में (\(A \cup B\)') का सही रूप दिया गया है?
Which option gives the correct form of (\(A \cup B\)')?
#sets
#de-morgan
#union
#complement
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A \(A' \cap B'\)
B \(A' \cup B'\)
C \(A \cap B'\)
D \(A' \cup B\)
Explanation opens after your attempt
Correct Answer
A. \(A' \cap B'\)
Step 1
Concept
The complement of a union equals the intersection of the complements. This is a direct use of De Morgan's law.
Step 2
Why this answer is correct
The correct answer is A. \(A' \cap B'\). The complement of a union equals the intersection of the complements. This is a direct use of De Morgan's law.
Step 3
Exam Tip
संघ का पूरक पूरकों के प्रतिच्छेद के बराबर होता है। यह डी मॉर्गन नियम का सीधा प्रयोग है।
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यदि \(U={1,2,\ldots,18}\), \(A=\{2,3,5,7,11,13,17\}\) और \(B=\{1,4,9,16\}\), तो (\(A \cup B\)') क्या है?
If \(U={1,2,\ldots,18}\), \(A=\{2,3,5,7,11,13,17\}\), and \(B=\{1,4,9,16\}\), what is (\(A \cup B\)')?
#sets
#union
#complement
#finite-set
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A ({6,8,10,12,14,15,18})
B ({1,2,3,4,5,7,9,11,13,16,17})
C ({6,8,10,12,14,18})
D ({15})
Explanation opens after your attempt
Correct Answer
A. ({6,8,10,12,14,15,18})
Step 1
Concept
First form \(A \cup B\), then remove it from (U). The remaining elements are ({6,8,10,12,14,15,18}).
Step 2
Why this answer is correct
The correct answer is A. ({6,8,10,12,14,15,18}). First form \(A \cup B\), then remove it from (U). The remaining elements are ({6,8,10,12,14,15,18}).
Step 3
Exam Tip
पहले \(A \cup B\) बनाएं और फिर उसे (U) से हटाएं। शेष ({6,8,10,12,14,15,18}) हैं।
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यदि \(U=\mathbb{R}\) और (A=[-2,4)), तो (A') क्या है?
If \(U=\mathbb{R}\) and (A=[-2,4)), what is (A')?
#sets
#intervals
#complement
#boundary-points
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A (\(-\infty,-2\) \cup [4,\infty))
B ((-\infty,-2] \cup \(4,\infty\))
C (\(-\infty,-2\) \cup \(4,\infty\))
D ([-2,4))
Explanation opens after your attempt
Correct Answer
A. (\(-\infty,-2\) \cup [4,\infty))
Step 1
Concept
(-2) is in (A), so it is not in the complement, while (4) is not in (A), so it is in the complement.
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,-2\) \cup [4,\infty)). (-2) is in (A), so it is not in the complement, while (4) is not in (A), so it is in the complement.
Step 3
Exam Tip
(-2) समुच्चय (A) में है इसलिए पूरक में नहीं आएगा, पर (4) (A) में नहीं है इसलिए पूरक में आएगा।
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यदि (n(U)=120), (n(A')=47), तो (n(A)) क्या है?
If (n(U)=120) and (n(A')=47), what is (n(A))?
#sets
#cardinality
#complement
#basic-numerical
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A (73)
B (47)
C (167)
D (120)
Explanation opens after your attempt
Step 1
Concept
Since (A) and (A') together form (U), (n(A)=120-47=73). Subtract the given complement count directly.
Step 2
Why this answer is correct
The correct answer is A. (73). Since (A) and (A') together form (U), (n(A)=120-47=73). Subtract the given complement count directly.
Step 3
Exam Tip
क्योंकि (A) और (A') मिलकर (U) बनाते हैं, (n(A)=120-47=73)। पूरक में दिए गए आंकड़े को सीधे घटाएं।
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यदि \(A \cap B=\varnothing\), तो (B) के बारे में कौन सा कथन अवश्य सत्य है?
If \(A \cap B=\varnothing\), which statement about (B) must be true?
#sets
#disjoint-sets
#complement
#subset
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A \(B \subseteq A'\)
B \(A \subseteq B'\) गलत है / \(A \subseteq B'\) is false
C (B=A')
D \(A \cup B=U\)
Explanation opens after your attempt
Correct Answer
A. \(B \subseteq A'\)
Step 1
Concept
If no element of (B) lies in (A), every element of (B) lies in (A'). Hence \(B \subseteq A'\) must be true.
Step 2
Why this answer is correct
The correct answer is A. \(B \subseteq A'\). If no element of (B) lies in (A), every element of (B) lies in (A'). Hence \(B \subseteq A'\) must be true.
Step 3
Exam Tip
यदि (B) का कोई सदस्य (A) में नहीं है, तो हर सदस्य (A') में होगा। इसलिए \(B \subseteq A'\) अवश्य सत्य है।
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\(यदि (U={1,2,\ldots,24}), (A={x:x \in U\) तथा x सम है\(}), (B={x:x \in U\) तथा x विषम है}), तो (A') और (B) का संबंध क्या है?
\(If (U={1,2,\ldots,24}), (A={x:x \in U\) and x is even\(}), and (B={x:x \in U\) and x is odd}), what is the relation between (A') and (B)?
#sets
#even-odd
#complement
#equality
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A (A'=B)
B \(A' \subset B\)
C \(A' \cap B=\varnothing\)
D (A'=U)
Explanation opens after your attempt
Step 1
Concept
The complement of even numbers in (U) is the set of odd numbers. Therefore (A'=B).
Step 2
Why this answer is correct
The correct answer is A. (A'=B). The complement of even numbers in (U) is the set of odd numbers. Therefore (A'=B).
Step 3
Exam Tip
(U) में सम संख्याओं का पूरक विषम संख्याएं हैं। इसलिए (A'=B) है।
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\(यदि (U={1,2,\ldots,40}), (A={x:x \in U\) तथा \(2 \mid x}), (B={x:x \in U\) तथा \(5 \mid x}), तो (n(A' \cap B')) क्या है\)?
\(If (U={1,2,\ldots,40}), (A={x:x \in U\) and \(2 \mid x}), and (B={x:x \in U\) and \(5 \mid x}), what is (n(A' \cap B'))\)?
#sets
#de-morgan
#cardinality
#divisibility
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A (16)
B (24)
C (20)
D (4)
Explanation opens after your attempt
Step 1
Concept
(A' \cap B'=\(A \cup B\)'). Numbers divisible by (2) or (5) are (24), so the complement is (40-24=16).
Step 2
Why this answer is correct
The correct answer is A. (16). (A' \cap B'=\(A \cup B\)'). Numbers divisible by (2) or (5) are (24), so the complement is (40-24=16).
Step 3
Exam Tip
(A' \cap B'=\(A \cup B\)') है। (2) या (5) से विभाज्य संख्याएं (24) हैं, इसलिए पूरक (40-24=16) है।
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\(यदि (U={x:x \in \mathbb{Z}, -3 \le x \le 7}) और (A={x:x \in U\) तथा \(x+2>4}), तो (A') क्या है\)?
\(If (U={x:x \in \mathbb{Z}, -3 \le x \le 7}) and (A={x:x \in U\) and \(x+2>4}), what is (A')\)?
#sets
#complement
#linear-inequality
#integers
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A ({-3,-2,-1,0,1,2})
B ({3,4,5,6,7})
C ({-3,-2,-1,0,1})
D ({2,3,4,5,6,7})
Explanation opens after your attempt
Correct Answer
A. ({-3,-2,-1,0,1,2})
Step 1
Concept
(x+2>4) gives (x>2), so \(A=\{3,4,5,6,7\}\). The complement contains the remaining integers.
Step 2
Why this answer is correct
The correct answer is A. ({-3,-2,-1,0,1,2}). (x+2>4) gives (x>2), so \(A=\{3,4,5,6,7\}\). The complement contains the remaining integers.
Step 3
Exam Tip
(x+2>4) से (x>2) मिलता है, इसलिए \(A=\{3,4,5,6,7\}\) है। पूरक बाकी पूर्णांक हैं।
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यदि \(A-B=A \cap B'\) है, तो ((A-B)') किसके बराबर होगा?
If \(A-B=A \cap B'\), what is ((A-B)') equal to?
#sets
#difference
#complement
#de-morgan
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A \(A' \cup B\)
B \(A' \cap B\)
C \(A \cup B'\)
D \(A \cap B\)
Explanation opens after your attempt
Correct Answer
A. \(A' \cup B\)
Step 1
Concept
((A-B)'=\(A \cap B'\)'=A' \cup (B')'). Therefore the answer is \(A' \cup B\).
Step 2
Why this answer is correct
The correct answer is A. \(A' \cup B\). ((A-B)'=\(A \cap B'\)'=A' \cup (B')'). Therefore the answer is \(A' \cup B\).
Step 3
Exam Tip
((A-B)'=\(A \cap B'\)'=A' \cup (B')') होता है। इसलिए उत्तर \(A' \cup B\) है।
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यदि \(U=\mathbb{R}\), (A=\(-\infty,1\)) और (B=\(4,\infty\)), तो (\(A \cup B\)') क्या है?
If \(U=\mathbb{R}\), (A=\(-\infty,1\)), and (B=\(4,\infty\)), what is (\(A \cup B\)')?
#sets
#intervals
#union
#complement
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A ([1,4])
B ((1,4))
C ([1,4))
D ((1,4])
Explanation opens after your attempt
Correct Answer
A. ([1,4])
Step 1
Concept
The set \(A \cup B\) does not include (1) and (4). Hence the complement includes both endpoints, giving ([1,4]).
Step 2
Why this answer is correct
The correct answer is A. ([1,4]). The set \(A \cup B\) does not include (1) and (4). Hence the complement includes both endpoints, giving ([1,4]).
Step 3
Exam Tip
\(A \cup B\) में (1) और (4) शामिल नहीं हैं। इसलिए पूरक में दोनों सिरों सहित ([1,4]) आएगा।
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कौन सा कथन (A) के पूरक के लिए गलत है?
Which statement is false for the complement of (A)?
#sets
#conceptual
#error-identification
#complement
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A (A') सार्वत्रिक समुच्चय से स्वतंत्र होता है / (A') is independent of the universal set
B \(A \cup A'=U\)
C \(A \cap A'=\varnothing\)
D (A'=U-A)
Explanation opens after your attempt
Correct Answer
A. (A') सार्वत्रिक समुच्चय से स्वतंत्र होता है / (A') is independent of the universal set
Step 1
Concept
The complement depends on the universal set. So (A') cannot be fixed without knowing (U).
Step 2
Why this answer is correct
The correct answer is A. (A') सार्वत्रिक समुच्चय से स्वतंत्र होता है / (A') is independent of the universal set. The complement depends on the universal set. So (A') cannot be fixed without knowing (U).
Step 3
Exam Tip
पूरक सार्वत्रिक समुच्चय पर निर्भर करता है। इसलिए (A') को (U) बताए बिना निश्चित नहीं किया जा सकता।
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\(यदि (U={1,2,\ldots,16}) और (A={x:x \in U\) तथा x का कोई भाजक 4 है}), तो (A') क्या है?
\(If (U={1,2,\ldots,16}) and (A={x:x \in U\) and 4 is a divisor of x}), what is (A')?
#sets
#divisibility
#complement
#finite-set
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A ({1,2,3,5,6,7,9,10,11,13,14,15})
B ({4,8,12,16})
C ({1,2,3,4,5,6,7,8})
D ({2,6,10,14})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,5,6,7,9,10,11,13,14,15})
Step 1
Concept
(A) contains the multiples of (4), namely ({4,8,12,16}). All remaining elements belong to (A').
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,5,6,7,9,10,11,13,14,15}). (A) contains the multiples of (4), namely ({4,8,12,16}). All remaining elements belong to (A').
Step 3
Exam Tip
(A) में (4) के गुणज ({4,8,12,16}) हैं। बाकी सभी सदस्य (A') में होंगे।
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यदि \(A \subseteq U\), तो ((U-A)') किसके बराबर है?
If \(A \subseteq U\), what is ((U-A)') equal to?
#sets
#difference
#double-complement
#identity
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A (A)
B (A')
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
(U-A=A'). Therefore ((U-A)'=(A')'=A).
Step 2
Why this answer is correct
The correct answer is A. (A). (U-A=A'). Therefore ((U-A)'=(A')'=A).
Step 3
Exam Tip
(U-A=A') होता है। इसलिए ((U-A)'=(A')'=A) है।
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\(यदि (U={x:x \in \mathbb{N}, x \le 60}), (A={x:x \in U\) तथा \(3 \mid x}) और (B={x:x \in U\) तथा \(4 \mid x}), तो (n((A \cap B)')) क्या है\)?
\(If (U={x:x \in \mathbb{N}, x \le 60}), (A={x:x \in U\) and \(3 \mid x}), and (B={x:x \in U\) and \(4 \mid x}), what is (n((A \cap B)'))\)?
#sets
#cardinality
#lcm
#complement
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A (55)
B (5)
C (40)
D (45)
Explanation opens after your attempt
Step 1
Concept
\(A \cap B\) contains multiples of (12), and there are (5) up to (60). Hence the complement is (60-5=55).
Step 2
Why this answer is correct
The correct answer is A. (55). \(A \cap B\) contains multiples of (12), and there are (5) up to (60). Hence the complement is (60-5=55).
Step 3
Exam Tip
\(A \cap B\) में (12) के गुणज होंगे और (60) तक ऐसे (5) हैं। इसलिए पूरक (60-5=55) है।
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यदि \(U={1,2,\ldots,8}\), \(A=\{1,2,5\}\), \(B=\{2,4,6\}\), तो \(A' \cup B'\) क्या है?
If \(U={1,2,\ldots,8}\), \(A=\{1,2,5\}\), and \(B=\{2,4,6\}\), what is \(A' \cup B'\)?
#sets
#de-morgan
#union-of-complements
#finite-set
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A ({1,3,4,5,6,7,8})
B ({2})
C ({3,7,8})
D ({1,2,4,5,6})
Explanation opens after your attempt
Correct Answer
A. ({1,3,4,5,6,7,8})
Step 1
Concept
By De Morgan, (A' \cup B'=\(A \cap B\)'). Since \(A \cap B={2}\), the complement is ({1,3,4,5,6,7,8}).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,4,5,6,7,8}). By De Morgan, (A' \cup B'=\(A \cap B\)'). Since \(A \cap B={2}\), the complement is ({1,3,4,5,6,7,8}).
Step 3
Exam Tip
डी मॉर्गन से (A' \cup B'=\(A \cap B\)') है। \(A \cap B={2}\), इसलिए पूरक ({1,3,4,5,6,7,8}) है।
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यदि \(U=\mathbb{R}\) और \(A={x:x \in \mathbb{R}, -1<x\le 6}\), तो (A') क्या है?
If \(U=\mathbb{R}\) and \(A={x:x \in \mathbb{R}, -1<x\le 6}\), what is (A')?
#sets
#real-numbers
#interval-complement
#boundary
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A ((-\infty,-1] \cup \(6,\infty\))
B (\(-\infty,-1\) \cup [6,\infty))
C ([-1,6])
D ((-1,6])
Explanation opens after your attempt
Correct Answer
A. ((-\infty,-1] \cup \(6,\infty\))
Step 1
Concept
The point (-1) is not in (A), so it is included in the complement, while (6) is in (A), so it is excluded.
Step 2
Why this answer is correct
The correct answer is A. ((-\infty,-1] \cup \(6,\infty\)). The point (-1) is not in (A), so it is included in the complement, while (6) is in (A), so it is excluded.
Step 3
Exam Tip
(-1) (A) में नहीं है इसलिए पूरक में शामिल है, जबकि (6) (A) में है इसलिए पूरक में नहीं है।
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\(यदि (U={1,2,\ldots,25}), (A={x:x \in U\) तथा x अभाज्य नहीं है}), तो (A') क्या है?
\(If (U={1,2,\ldots,25}), (A={x:x \in U\) and x is not prime}), what is (A')?
#sets
#prime-numbers
#complement
#conceptual
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A ({2,3,5,7,11,13,17,19,23})
B ({1,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25})
C ({1,2,3,5,7,11,13,17,19,23})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({2,3,5,7,11,13,17,19,23})
Step 1
Concept
If (A) contains non-prime numbers, then (A') contains prime numbers. Remember that (1) is not prime.
Step 2
Why this answer is correct
The correct answer is A. ({2,3,5,7,11,13,17,19,23}). If (A) contains non-prime numbers, then (A') contains prime numbers. Remember that (1) is not prime.
Step 3
Exam Tip
यदि (A) में अभाज्य नहीं संख्याएं हैं, तो (A') में अभाज्य संख्याएं होंगी। (1) अभाज्य नहीं है।
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यदि (A) और (B) ऐसे हैं कि \(A \cup B=U\), तो (A') के लिए कौन सा कथन सही है?
If (A) and (B) satisfy \(A \cup B=U\), which statement about (A') is correct?
#sets
#union
#subset
#complement-reasoning
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A \(A' \subseteq B\)
B \(B \subseteq A'\)
C (A'=B) अवश्य / (A'=B) necessarily
D \(A'=\varnothing\) अवश्य / \(A'=\varnothing\) necessarily
Explanation opens after your attempt
Correct Answer
A. \(A' \subseteq B\)
Step 1
Concept
Elements not in (A) must be in (B) because \(A \cup B=U\). Hence \(A' \subseteq B\).
Step 2
Why this answer is correct
The correct answer is A. \(A' \subseteq B\). Elements not in (A) must be in (B) because \(A \cup B=U\). Hence \(A' \subseteq B\).
Step 3
Exam Tip
जो सदस्य (A) में नहीं हैं, वे \(A \cup B=U\) के कारण (B) में होने चाहिए। इसलिए \(A' \subseteq B\) है।
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यदि \(U={1,2,\ldots,12}\), \(A=\{1,2,3,4,5\}\), तो \(A' \cup A\) क्या है?
If \(U={1,2,\ldots,12}\), \(A=\{1,2,3,4,5\}\), what is \(A' \cup A\)?
#sets
#identity
#complement
#universal-set
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A (U)
B (A)
C (A')
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The union of any set with its complement gives the whole (U). This is the basic identity of complement.
Step 2
Why this answer is correct
The correct answer is A. (U). The union of any set with its complement gives the whole (U). This is the basic identity of complement.
Step 3
Exam Tip
किसी भी समुच्चय का अपने पूरक के साथ संघ पूरा (U) देता है। यह पूरक की मूल पहचान है।
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यदि \(U=\{a,b,c,d,e,g,h\}\) और \(A=\{a,e,h\}\), तो (A') क्या है?
If \(U=\{a,b,c,d,e,g,h\}\) and \(A=\{a,e,h\}\), what is (A')?
#sets
#letters
#universal-set
#complement
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A ({b,c,d,g})
B ({a,e,h})
C ({b,c,d,f,g})
D ({a,b,c,d,e,g,h})
Explanation opens after your attempt
Correct Answer
A. ({b,c,d,g})
Step 1
Concept
The complement contains only those letters of (U) that are not in (A). Do not add (f) because \(f \notin U\).
Step 2
Why this answer is correct
The correct answer is A. ({b,c,d,g}). The complement contains only those letters of (U) that are not in (A). Do not add (f) because \(f \notin U\).
Step 3
Exam Tip
पूरक में केवल (U) के वे अक्षर आएंगे जो (A) में नहीं हैं। (f) को नहीं जोड़ना क्योंकि \(f \notin U\) है।
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\(यदि (U={1,2,\ldots,30}), (A={x:x \in U\) तथा x का अंतिम अंक 0 या 5 है}), तो (n(A')) क्या है?
\(If (U={1,2,\ldots,30}), (A={x:x \in U\) and the last digit of x is 0 or 5}), what is (n(A'))?
#sets
#complement
#counting
#multiples-of-five
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A (24)
B (6)
C (25)
D (20)
Explanation opens after your attempt
Step 1
Concept
(A) has (6) elements: (5,10,15,20,25,30). Therefore (n(A')=30-6=24).
Step 2
Why this answer is correct
The correct answer is A. (24). (A) has (6) elements: (5,10,15,20,25,30). Therefore (n(A')=30-6=24).
Step 3
Exam Tip
(A) में (5,10,15,20,25,30) यानी (6) सदस्य हैं। इसलिए (n(A')=30-6=24) है।
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यदि \(A \subseteq U\), तो \(A \cap U'\) किसके बराबर होगा?
If \(A \subseteq U\), what is \(A \cap U'\) equal to?
#sets
#universal-set
#empty-set
#complement
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A \(\varnothing\)
B (A)
C (U)
D (A')
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\)
Step 1
Concept
The complement of the universal set (U) is \(\varnothing\). Hence \(A \cap U' = A \cap \varnothing=\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). The complement of the universal set (U) is \(\varnothing\). Hence \(A \cap U' = A \cap \varnothing=\varnothing\).
Step 3
Exam Tip
सार्वत्रिक समुच्चय (U) का पूरक \(\varnothing\) होता है। इसलिए \(A \cap U' = A \cap \varnothing=\varnothing\) है।
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यदि \(U=\mathbb{R}\), \(A={x:x \in \mathbb{R}, x \ne 0}\), तो (A') क्या है?
If \(U=\mathbb{R}\), \(A={x:x \in \mathbb{R}, x \ne 0}\), what is (A')?
#sets
#real-numbers
#complement
#singleton
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A ({0})
B \(\mathbb{R}\)
C \(\varnothing\)
D \(\mathbb{R}-{1}\)
Explanation opens after your attempt
Step 1
Concept
(A) contains all real numbers except (0). Therefore (A') is only ({0}).
Step 2
Why this answer is correct
The correct answer is A. ({0}). (A) contains all real numbers except (0). Therefore (A') is only ({0}).
Step 3
Exam Tip
(A) में सभी वास्तविक संख्याएं हैं लेकिन (0) नहीं है। इसलिए (A') केवल ({0}) है।
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\(यदि (U={1,2,\ldots,20}), (A={x:x \in U\) तथा \(x \le 8}) और (B={x:x \in U\) तथा \(x \ge 14}), तो ((A \cup B)') क्या है\)?
\(If (U={1,2,\ldots,20}), (A={x:x \in U\) and \(x \le 8}), and (B={x:x \in U\) and \(x \ge 14}), what is ((A \cup B)')\)?
#sets
#union
#complement
#range
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A ({9,10,11,12,13})
B ({1,2,3,4,5,6,7,8,14,15,16,17,18,19,20})
C ({8,9,10,11,12,13,14})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({9,10,11,12,13})
Step 1
Concept
\(A \cup B\) contains elements from (1) to (8) and from (14) to (20). The middle elements from (9) to (13) remain in the complement.
Step 2
Why this answer is correct
The correct answer is A. ({9,10,11,12,13}). \(A \cup B\) contains elements from (1) to (8) and from (14) to (20). The middle elements from (9) to (13) remain in the complement.
Step 3
Exam Tip
\(A \cup B\) में (1) से (8) और (14) से (20) तक के सदस्य हैं। बीच के (9) से (13) तक पूरक में बचते हैं।
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\(यदि (U={x:x \in \mathbb{Z}, -10 \le x \le 10}) और (A={x:x \in U\) तथा \(|x|\le 3}), तो (n(A')) क्या है\)?
\(If (U={x:x \in \mathbb{Z}, -10 \le x \le 10}) and (A={x:x \in U\) and \(|x|\le 3}), what is (n(A'))\)?
#sets
#absolute-value
#complement
#cardinality
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A (14)
B (7)
C (13)
D (21)
Explanation opens after your attempt
Step 1
Concept
There are (21) integers in (U), and \(A=\{-3,-2,-1,0,1,2,3\}\) has (7) elements. Thus (n(A')=21-7=14).
Step 2
Why this answer is correct
The correct answer is A. (14). There are (21) integers in (U), and \(A=\{-3,-2,-1,0,1,2,3\}\) has (7) elements. Thus (n(A')=21-7=14).
Step 3
Exam Tip
(U) में (21) पूर्णांक हैं और \(A=\{-3,-2,-1,0,1,2,3\}\) में (7) सदस्य हैं। अतः (n(A')=21-7=14) है।
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यदि \(U={1,2,\ldots,36}\), (A) (6) के गुणजों का समुच्चय है, तो (A') में से (12) के गुणजों की संख्या कितनी है?
If \(U={1,2,\ldots,36}\) and (A) is the set of multiples of (6), how many multiples of (12) are in (A')?
#sets
#complement
#multiples
#reasoning
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A (0)
B (3)
C (6)
D (33)
Explanation opens after your attempt
Step 1
Concept
Every multiple of (12) is also a multiple of (6), so it lies in (A). Hence no multiple of (12) lies in (A').
Step 2
Why this answer is correct
The correct answer is A. (0). Every multiple of (12) is also a multiple of (6), so it lies in (A). Hence no multiple of (12) lies in (A').
Step 3
Exam Tip
हर (12) का गुणज (6) का भी गुणज होता है, इसलिए वह (A) में होगा। अतः (A') में (12) का कोई गुणज नहीं होगा।
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यदि \(U=\mathbb{R}\), (A=\(-\infty,0]\) और \(B=[2,\infty\)), तो \(A' \cap B'\) क्या है?
If \(U=\mathbb{R}\), (A=\(-\infty,0]\), and \(B=[2,\infty\)), what is \(A' \cap B'\)?
#sets
#intervals
#intersection-of-complements
#de-morgan
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A ((0,2))
B ([0,2])
C (\(-\infty,0] \cup [2,\infty\))
D (\(0,\infty\))
Explanation opens after your attempt
Correct Answer
A. ((0,2))
Step 1
Concept
(A'=\(0,\infty\)) and (B'=\(-\infty,2\)). Their intersection is ((0,2)).
Step 2
Why this answer is correct
The correct answer is A. ((0,2)). (A'=\(0,\infty\)) and (B'=\(-\infty,2\)). Their intersection is ((0,2)).
Step 3
Exam Tip
(A'=\(0,\infty\)) और (B'=\(-\infty,2\)) हैं। उनका प्रतिच्छेद ((0,2)) है।
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\(यदि (U={1,2,\ldots,10}) और (A={x:x \in U\) तथा \(x^2-11x+30=0}), तो (A' \cap {5,6,7,8}) क्या है\)?
\(If (U={1,2,\ldots,10}) and (A={x:x \in U\) and \(x^2-11x+30=0}), what is (A' \cap {5,6,7,8})\)?
#sets
#quadratic
#complement
#intersection
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A ({7,8})
B ({5,6})
C ({5,6,7,8})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({7,8})
Step 1
Concept
The equation gives \(A=\{5,6\}\), so (5) and (6) are not in (A'). From the given set, ({7,8}) remains.
Step 2
Why this answer is correct
The correct answer is A. ({7,8}). The equation gives \(A=\{5,6\}\), so (5) and (6) are not in (A'). From the given set, ({7,8}) remains.
Step 3
Exam Tip
समीकरण से \(A=\{5,6\}\) मिलता है, इसलिए (A') में (5) और (6) नहीं होंगे। दिए गए समुच्चय से ({7,8}) बचता है।
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