यदि \(A=\{1,2,3,4\}\) और सार्वत्रिक समुच्चय \(U=\{1,2,3,4,5,6\}\) है, तो (P(A')) में अवयवों की संख्या क्या होगी?
If \(A=\{1,2,3,4\}\) and the universal set is \(U=\{1,2,3,4,5,6\}\), then what is the number of elements in (P(A'))?
#sets
#power-set
#universal-set
#complement
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A (2)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
(A'=U-A={5,6}), so (n(P(A'))=22 =4). In exams find the complement first.
Step 2
Why this answer is correct
The correct answer is B. (4). (A'=U-A={5,6}), so (n(P(A'))=22 =4). In exams find the complement first.
Step 3
Exam Tip
(A'=U-A={5,6}), इसलिए (n(P(A'))=22 =4)। परीक्षा में पहले पूरक समुच्चय निकालें।
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\(यदि (U={1,2,3,4,5,6,7,8,9,10}) और (A={x:x\in U,\ x\) सम संख्या है}), तो (P(A')) के कितने अवयवों में ठीक (2) अवयव होंगे?
\(If (U={1,2,3,4,5,6,7,8,9,10}) and (A={x:x\in U,\ x\) is an even number}), then how many elements of (P(A')) will have exactly (2) elements?
#sets
#power-set
#universal-set
#combination
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A (5)
B (10)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
(A'={1,3,5,7,9}), so the subsets with exactly (2) elements are \(\binom{5}{2}=10\). First find the complement set and then use combinations.
Step 2
Why this answer is correct
The correct answer is B. (10). (A'={1,3,5,7,9}), so the subsets with exactly (2) elements are \(\binom{5}{2}=10\). First find the complement set and then use combinations.
Step 3
Exam Tip
(A'={1,3,5,7,9}), इसलिए ठीक (2) अवयव वाले उपसमुच्चय \(\binom{5}{2}=10\) होंगे। पहले पूरक समुच्चय निकालें फिर संयोजन लगाएं।
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यदि (n(P(P(A)))=256), तो (n(A)) का मान क्या है?
If (n(P(P(A)))=256), then what is the value of (n(A))?
#sets
#power-set
#nested-power-set
#cardinality
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
If (n(A)=m), then (n(P(P(A)))=2^{2^m}=256=28 ), so \(2^m=8\) and (m=3). Compare powers directly.
Step 2
Why this answer is correct
The correct answer is B. (3). If (n(A)=m), then (n(P(P(A)))=2^{2^m}=256=28 ), so \(2^m=8\) and (m=3). Compare powers directly.
Step 3
Exam Tip
यदि (n(A)=m), तो (n(P(P(A)))=2^{2^m}=256=28 ), इसलिए \(2^m=8\) और (m=3)। घातों की तुलना सीधे करें।
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सार्वत्रिक समुच्चय \(U={x:x\in \mathbb{N},1\le x\le 10}\) और \(A=\{2,4,6,8,10\}\) है। (P(A')) में कितने एकल समुच्चय होंगे?
The universal set is \(U={x:x\in \mathbb{N},1\le x\le 10}\) and \(A=\{2,4,6,8,10\}\). How many singleton sets are in (P(A'))?
#sets
#power-set
#universal-set
#singleton
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A (4)
B (5)
C (10)
D (32)
Explanation opens after your attempt
Step 1
Concept
(A'={1,3,5,7,9}), and singleton sets in (P(A')) are (n(A')=5). The number of singleton subsets equals the number of elements.
Step 2
Why this answer is correct
The correct answer is B. (5). (A'={1,3,5,7,9}), and singleton sets in (P(A')) are (n(A')=5). The number of singleton subsets equals the number of elements.
Step 3
Exam Tip
(A'={1,3,5,7,9}) और (P(A')) में एकल समुच्चय (n(A')=5) होते हैं। एकल उपसमुच्चयों की संख्या मूल अवयवों जितनी होती है।
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यदि \(A\subseteq U\), (n(U)=9), (n(A)=4), तो (P(A')) के उचित उपसमुच्चयों की संख्या क्या है?
If \(A\subseteq U\), (n(U)=9), and (n(A)=4), then what is the number of proper subsets of (P(A'))?
#sets
#power-set
#proper-subset
#expert
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A (31)
B (32)
C (1023)
D (1024)
Explanation opens after your attempt
Step 1
Concept
(n(A')=5), so (n(P(A'))=25 =32). Proper subsets of (P(A')) are \(2^{32}-1\), so do not confuse elements with subsets.
Step 2
Why this answer is correct
The correct answer is C. (1023). (n(A')=5), so (n(P(A'))=25 =32). Proper subsets of (P(A')) are \(2^{32}-1\), so do not confuse elements with subsets.
Step 3
Exam Tip
(n(A')=5), इसलिए (n(P(A'))=25 =32)। इसके उचित उपसमुच्चय \(2^{32}-1\) नहीं बल्कि (P(A')) के उपसमुच्चय हैं, अतः \(2^{32}-1\) होगा।
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यदि (P(A)=P(B)), तो सही निष्कर्ष कौन सा है?
If (P(A)=P(B)), which conclusion is correct?
#sets
#power-set
#equality
#concept
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A \(A\cap B=\varnothing\)
B (A=B)
C \(A\subset B\)
D \(A\in B\)
Explanation opens after your attempt
Step 1
Concept
A power set uniquely determines its original set, so (A=B). Equal power sets mean equal original sets.
Step 2
Why this answer is correct
The correct answer is B. (A=B). A power set uniquely determines its original set, so (A=B). Equal power sets mean equal original sets.
Step 3
Exam Tip
किसी समुच्चय का पावर सेट उस समुच्चय को पूरी तरह निर्धारित करता है, इसलिए (A=B)। समान पावर सेट का मतलब समान मूल समुच्चय होता है।
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यदि \(A=\varnothing\), तो (P(P(A))) क्या होगा?
If \(A=\varnothing\), then what is (P(P(A)))?
#sets
#power-set
#empty-set
#nested
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A \(\varnothing\)
B \({\varnothing}\)
C \({{\varnothing}}\)
D \({\varnothing,{\varnothing}}\)
Explanation opens after your attempt
Correct Answer
D. \({\varnothing,{\varnothing}}\)
Step 1
Concept
(P\(\varnothing\)={\varnothing}), so (P(P(A))=P\({\varnothing}\)={\varnothing,{\varnothing}}). The power set of an empty set is not empty.
Step 2
Why this answer is correct
The correct answer is D. \({\varnothing,{\varnothing}}\). (P\(\varnothing\)={\varnothing}), so (P(P(A))=P\({\varnothing}\)={\varnothing,{\varnothing}}). The power set of an empty set is not empty.
Step 3
Exam Tip
(P\(\varnothing\)={\varnothing}), इसलिए (P(P(A))=P\({\varnothing}\)={\varnothing,{\varnothing}})। खाली समुच्चय का पावर सेट खाली नहीं होता।
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यदि \(U=\{a,b,c,d,e\}\), \(A=\{a,c\}\) और \(B=\{c,d\}\), तो (P(\(A\cup B\)')) के अवयवों की संख्या क्या है?
If \(U=\{a,b,c,d,e\}\), \(A=\{a,c\}\), and \(B=\{c,d\}\), then what is the number of elements of (P(\(A\cup B\)'))?
#sets
#power-set
#union
#complement
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A (2)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B={a,c,d}\) and (\(A\cup B\)'={b,e}), so the power set has \(2^2=4\) elements. Find the union first.
Step 2
Why this answer is correct
The correct answer is B. (4). \(A\cup B={a,c,d}\) and (\(A\cup B\)'={b,e}), so the power set has \(2^2=4\) elements. Find the union first.
Step 3
Exam Tip
\(A\cup B={a,c,d}\) और (\(A\cup B\)'={b,e}), इसलिए पावर सेट में \(2^2=4\) अवयव हैं। पहले संघ निकालना सुरक्षित रहता है।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6\}\), तो (n(P\(A'\cap B'\))) क्या है?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4\}\), and \(B=\{3,4,5,6\}\), then what is (n(P\(A'\cap B'\)))?
#sets
#power-set
#de-morgan
#universal-set
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A (2)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
(A'\cap B'=\(A\cup B\)'={7,8}), so (n(P\(A'\cap B'\))=22 =4). De Morgan's law saves time.
Step 2
Why this answer is correct
The correct answer is B. (4). (A'\cap B'=\(A\cup B\)'={7,8}), so (n(P\(A'\cap B'\))=22 =4). De Morgan's law saves time.
Step 3
Exam Tip
(A'\cap B'=\(A\cup B\)'={7,8}), इसलिए (n(P\(A'\cap B'\))=22 =4)। डी मॉर्गन नियम से समय बचता है।
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यदि \(A=\{p,q,r\}\), तो (P(A)) के उन अवयवों की संख्या कितनी है जिनमें (p) अवश्य हो?
If \(A=\{p,q,r\}\), how many elements of (P(A)) must contain (p)?
#sets
#power-set
#counting
#compulsory-element
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
After fixing (p), the remaining (q,r) have \(2^2=4\) choices. Treat the compulsory element as fixed.
Step 2
Why this answer is correct
The correct answer is C. (4). After fixing (p), the remaining (q,r) have \(2^2=4\) choices. Treat the compulsory element as fixed.
Step 3
Exam Tip
(p) को स्थिर रखने पर बाकी (q,r) के \(2^2=4\) चयन होंगे। अनिवार्य अवयव को स्थिर मानें।
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यदि \(A=\{1,2,3,4,5\}\), तो (P(A)) के कितने अवयवों में ठीक (3) अवयव होंगे?
If \(A=\{1,2,3,4,5\}\), how many elements of (P(A)) have exactly (3) elements?
#sets
#power-set
#combination
#cardinality
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A (5)
B (10)
C (15)
D (20)
Explanation opens after your attempt
Step 1
Concept
Subsets with exactly (3) elements are \(\binom{5}{3}=10\). Use combinations for size-based counting in a power set.
Step 2
Why this answer is correct
The correct answer is B. (10). Subsets with exactly (3) elements are \(\binom{5}{3}=10\). Use combinations for size-based counting in a power set.
Step 3
Exam Tip
ठीक (3) अवयव वाले उपसमुच्चय \(\binom{5}{3}=10\) होते हैं। पावर सेट में आकार आधारित गिनती के लिए संयोजन लगाएं।
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यदि \(A=\{1,2,3,4\}\), तो (P(A)) के कितने अवयवों में (1) हो और (4) न हो?
If \(A=\{1,2,3,4\}\), how many elements of (P(A)) contain (1) but do not contain (4)?
#sets
#power-set
#counting
#conditional-subsets
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(1) is fixed and (4) is excluded, so (2,3) have \(2^2=4\) choices. Fix the conditions first.
Step 2
Why this answer is correct
The correct answer is B. (4). (1) is fixed and (4) is excluded, so (2,3) have \(2^2=4\) choices. Fix the conditions first.
Step 3
Exam Tip
(1) स्थिर है और (4) हटाया गया है, इसलिए (2,3) के \(2^2=4\) चयन होंगे। शर्तों को पहले स्थिर करें।
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यदि \(A=\{a,b,c,d\}\), तो (P(A)) के उन अवयवों की संख्या क्या है जो खाली समुच्चय नहीं हैं?
If \(A=\{a,b,c,d\}\), what is the number of elements of (P(A)) that are not empty sets?
#sets
#power-set
#non-empty-subsets
#counting
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A (15)
B (16)
C (14)
D (8)
Explanation opens after your attempt
Step 1
Concept
Total subsets are \(2^4=16\) and one subset is empty, so there are (15) non-empty subsets. Subtract (1) for non-empty subsets.
Step 2
Why this answer is correct
The correct answer is A. (15). Total subsets are \(2^4=16\) and one subset is empty, so there are (15) non-empty subsets. Subtract (1) for non-empty subsets.
Step 3
Exam Tip
कुल उपसमुच्चय \(2^4=16\) हैं और खाली उपसमुच्चय (1) है, इसलिए (15) गैर-रिक्त उपसमुच्चय हैं। गैर-रिक्त के लिए (1) घटाएं।
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यदि \(A=\{x,y,z,w\}\), तो (P(A)) के कितने अवयव उचित उपसमुच्चय नहीं हैं?
If \(A=\{x,y,z,w\}\), how many elements of (P(A)) are not proper subsets of (A)?
#sets
#power-set
#proper-subset
#concept
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A (0)
B (1)
C (2)
D (15)
Explanation opens after your attempt
Step 1
Concept
The elements of (P(A)) are all subsets of (A), and only (A) itself is not a proper subset. A proper subset excludes the whole set.
Step 2
Why this answer is correct
The correct answer is B. (1). The elements of (P(A)) are all subsets of (A), and only (A) itself is not a proper subset. A proper subset excludes the whole set.
Step 3
Exam Tip
(P(A)) के अवयव (A) के सभी उपसमुच्चय हैं, जिनमें केवल (A) स्वयं उचित उपसमुच्चय नहीं है। उचित उपसमुच्चय में पूरा समुच्चय नहीं आता।
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यदि (n(A)=6), तो (P(A)) के अवयवों में सम संख्या वाले अवयवों के उपसमुच्चयों की संख्या क्या होगी?
If (n(A)=6), what is the number of elements of (P(A)) that are subsets with an even number of elements?
#sets
#power-set
#even-subsets
#expert-counting
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A (16)
B (31)
C (32)
D (64)
Explanation opens after your attempt
Step 1
Concept
For a (6)-element set, even-sized subsets are \(2^{6-1}=32\). Even-sized and odd-sized subsets are equal in number.
Step 2
Why this answer is correct
The correct answer is C. (32). For a (6)-element set, even-sized subsets are \(2^{6-1}=32\). Even-sized and odd-sized subsets are equal in number.
Step 3
Exam Tip
किसी (6) अवयव वाले समुच्चय में सम आकार के उपसमुच्चय \(2^{6-1}=32\) होते हैं। सम और विषम आकार वाले उपसमुच्चय बराबर होते हैं।
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यदि (n(A)=5), तो (P(A)) के विषम संख्या वाले अवयवों के उपसमुच्चयों की संख्या क्या है?
If (n(A)=5), what is the number of subsets in (P(A)) having an odd number of elements?
#sets
#power-set
#odd-subsets
#cardinality
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A (10)
B (15)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
Odd-sized subsets are \(2^{5-1}=16\). This identity helps in quick counting.
Step 2
Why this answer is correct
The correct answer is C. (16). Odd-sized subsets are \(2^{5-1}=16\). This identity helps in quick counting.
Step 3
Exam Tip
विषम आकार के उपसमुच्चय \(2^{5-1}=16\) होते हैं। यह पहचान तेज गिनती में मदद करती है।
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यदि \(A=\{1,2,3\}\), तो (P(A)) का कौन सा अवयव नहीं है?
If \(A=\{1,2,3\}\), which is not an element of (P(A))?
#sets
#power-set
#element-check
#common-mistake
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A ({1,2})
B \(\varnothing\)
C ({{1}})
D ({1,2,3})
Explanation opens after your attempt
Correct Answer
C. ({{1}})
Step 1
Concept
Elements of (P(A)) are subsets of (A), but ({{1}}) has element ({1}), which is not an element of (A). Watch the layers of braces carefully.
Step 2
Why this answer is correct
The correct answer is C. ({{1}}). Elements of (P(A)) are subsets of (A), but ({{1}}) has element ({1}), which is not an element of (A). Watch the layers of braces carefully.
Step 3
Exam Tip
(P(A)) के अवयव (A) के उपसमुच्चय होते हैं, लेकिन ({{1}}) में अवयव ({1}) है जो (A) का अवयव नहीं है। ब्रेसेस की परतें ध्यान से देखें।
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यदि \(A={\varnothing,{1}}\), तो (n(P(A))) क्या है?
If \(A={\varnothing,{1}}\), then what is (n(P(A)))?
#sets
#power-set
#empty-set
#braces
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
(A) has two elements, \(\varnothing\) and ({1}), so (n(P(A))=22 =4). The empty set can also be an element.
Step 2
Why this answer is correct
The correct answer is C. (4). (A) has two elements, \(\varnothing\) and ({1}), so (n(P(A))=22 =4). The empty set can also be an element.
Step 3
Exam Tip
(A) में दो अवयव \(\varnothing\) और ({1}) हैं, इसलिए (n(P(A))=22 =4)। खाली समुच्चय भी अवयव हो सकता है।
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यदि \(A={\varnothing,{\varnothing}}\), तो (P(A)) में कौन सा अवयव अवश्य होगा?
If \(A={\varnothing,{\varnothing}}\), which element must be in (P(A))?
#sets
#power-set
#empty-set
#nested-braces
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A \({{{\varnothing}}}\)
B \({\varnothing,{\varnothing}}\)
C \({\varnothing,\varnothing}\)
D \({{\varnothing,{\varnothing}}}\)
Explanation opens after your attempt
Correct Answer
B. \({\varnothing,{\varnothing}}\)
Step 1
Concept
Every set is an element of its power set, so \(A={\varnothing,{\varnothing}}\) is included. The original set is also in its power set.
Step 2
Why this answer is correct
The correct answer is B. \({\varnothing,{\varnothing}}\). Every set is an element of its power set, so \(A={\varnothing,{\varnothing}}\) is included. The original set is also in its power set.
Step 3
Exam Tip
हर समुच्चय स्वयं अपने पावर सेट का अवयव होता है, इसलिए \(A={\varnothing,{\varnothing}}\) शामिल है। पावर सेट में मूल समुच्चय भी आता है।
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यदि \(U={x:x\in \mathbb{Z},-2\le x\le 2}\) और \(A={x:x\in U,x^2=1}\), तो (n(P(A'))) क्या है?
If \(U={x:x\in \mathbb{Z},-2\le x\le 2}\) and \(A={x:x\in U,x^2=1}\), then what is (n(P(A')))?
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#power-set
#set-builder
#universal-set
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A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
\(U=\{-2,-1,0,1,2\}\) and \(A=\{-1,1\}\), so (A'={-2,0,2}). Thus (n(P(A'))=23 =8).
Step 2
Why this answer is correct
The correct answer is B. (8). \(U=\{-2,-1,0,1,2\}\) and \(A=\{-1,1\}\), so (A'={-2,0,2}). Thus (n(P(A'))=23 =8).
Step 3
Exam Tip
\(U=\{-2,-1,0,1,2\}\) और \(A=\{-1,1\}\), इसलिए (A'={-2,0,2})। अब (n(P(A'))=23 =8)।
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\(यदि (U={1,2,3,4,5,6,7,8,9}) और (A={x:x\in U,x\) अभाज्य है}), तो (P(A')) में कितने अवयव होंगे?
\(If (U={1,2,3,4,5,6,7,8,9}) and (A={x:x\in U,x\) is prime}), how many elements are in (P(A'))?
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#power-set
#prime-numbers
#complement
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A (16)
B (32)
C (64)
D (128)
Explanation opens after your attempt
Step 1
Concept
\(A=\{2,3,5,7\}\), so (A'={1,4,6,8,9}) and (n(P(A'))=25 =32). Do not treat (1) as prime.
Step 2
Why this answer is correct
The correct answer is B. (32). \(A=\{2,3,5,7\}\), so (A'={1,4,6,8,9}) and (n(P(A'))=25 =32). Do not treat (1) as prime.
Step 3
Exam Tip
\(A=\{2,3,5,7\}\), इसलिए (A'={1,4,6,8,9}) और (n(P(A'))=25 =32)। (1) को अभाज्य न मानें।
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यदि (A) में (4) अवयव हैं, तो (P(A)) के (2)-अवयवी उपसमुच्चयों की संख्या क्या है?
If (A) has (4) elements, what is the number of (2)-element subsets of (P(A))?
#sets
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#combinations
#nested-counting
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A (6)
B (16)
C (120)
D (256)
Explanation opens after your attempt
Step 1
Concept
(P(A)) has \(2^4=16\) elements, so its (2)-element subsets are \(\binom{16}{2}=120\). Treat (P(A)) as a new set here.
Step 2
Why this answer is correct
The correct answer is C. (120). (P(A)) has \(2^4=16\) elements, so its (2)-element subsets are \(\binom{16}{2}=120\). Treat (P(A)) as a new set here.
Step 3
Exam Tip
(P(A)) में \(2^4=16\) अवयव हैं, इसलिए इसके (2)-अवयवी उपसमुच्चय \(\binom{16}{2}=120\) हैं। यहां (P(A)) को नया समुच्चय मानें।
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यदि (n(P(A))=n(P(B))), तो कौन सा निष्कर्ष निश्चित रूप से सत्य है?
If (n(P(A))=n(P(B))), which conclusion is definitely true?
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#equality
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A (A=B)
B (n(A)=n(B))
C \(A\subseteq B\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Correct Answer
B. (n(A)=n(B))
Step 1
Concept
From (2^{n(A)}=2^{n(B)}), we get (n(A)=n(B)), but the sets need not be equal. Cardinality and equality are different ideas.
Step 2
Why this answer is correct
The correct answer is B. (n(A)=n(B)). From (2^{n(A)}=2^{n(B)}), we get (n(A)=n(B)), but the sets need not be equal. Cardinality and equality are different ideas.
Step 3
Exam Tip
(2^{n(A)}=2^{n(B)}) से (n(A)=n(B)) मिलता है, पर समुच्चय समान होना जरूरी नहीं। कार्डिनैलिटी और समानता अलग बातें हैं।
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यदि \(A=\{1,2\}\) और \(B=\{3,4\}\), तो \(P(A)\cap P(B)\) क्या है?
If \(A=\{1,2\}\) and \(B=\{3,4\}\), then what is \(P(A)\cap P(B)\)?
#sets
#power-set
#intersection
#disjoint-sets
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A \(\varnothing\)
B \({\varnothing}\)
C ({1,2,3,4})
D ({{1},{3}})
Explanation opens after your attempt
Correct Answer
B. \({\varnothing}\)
Step 1
Concept
Both power sets always contain the empty set, and no other subset is common here. For disjoint original sets, the common element is \(\varnothing\).
Step 2
Why this answer is correct
The correct answer is B. \({\varnothing}\). Both power sets always contain the empty set, and no other subset is common here. For disjoint original sets, the common element is \(\varnothing\).
Step 3
Exam Tip
दोनों पावर सेटों में खाली समुच्चय हमेशा होता है और कोई अन्य समान उपसमुच्चय नहीं है। असंबद्ध मूल समुच्चयों के लिए सामान्य अवयव \(\varnothing\) रहता है।
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सामान्यतः \(P(A)\cap P(B)\) किसके बराबर होता है?
In general, \(P(A)\cap P(B)\) is equal to what?
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A (P\(A\cup B\))
B (P\(A\cap B\))
C (P(A-B))
D (P(A'))
Explanation opens after your attempt
Correct Answer
B. (P\(A\cap B\))
Step 1
Concept
Sets that are subsets of both (A) and (B) are subsets of \(A\cap B\). Hence (P(A)\cap P(B)=P\(A\cap B\)).
Step 2
Why this answer is correct
The correct answer is B. (P\(A\cap B\)). Sets that are subsets of both (A) and (B) are subsets of \(A\cap B\). Hence (P(A)\cap P(B)=P\(A\cap B\)).
Step 3
Exam Tip
जो समुच्चय (A) और (B) दोनों के उपसमुच्चय हैं, वे \(A\cap B\) के उपसमुच्चय होते हैं। इसलिए (P(A)\cap P(B)=P\(A\cap B\))।
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कौन सा कथन सामान्यतः असत्य है?
Which statement is generally false?
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A (P(A)\cap P(B)=P\(A\cap B\))
B यदि \(A\subseteq B\), तो \(P(A)\subseteq P(B)\) / If \(A\subseteq B\), then \(P(A)\subseteq P(B)\)
C (P(A)\cup P(B)=P\(A\cup B\))
D \(\varnothing\in P(A)\)
Explanation opens after your attempt
Correct Answer
C. (P(A)\cup P(B)=P\(A\cup B\))
Step 1
Concept
\(P(A)\cup P(B)\) contains subsets of (A) or subsets of (B), while (P\(A\cup B\)) may contain mixed subsets. Do not use this as an identity without checking.
Step 2
Why this answer is correct
The correct answer is C. (P(A)\cup P(B)=P\(A\cup B\)). \(P(A)\cup P(B)\) contains subsets of (A) or subsets of (B), while (P\(A\cup B\)) may contain mixed subsets. Do not use this as an identity without checking.
Step 3
Exam Tip
\(P(A)\cup P(B)\) में केवल (A) या (B) के अलग-अलग उपसमुच्चय होते हैं, जबकि (P\(A\cup B\)) में मिश्रित उपसमुच्चय भी हो सकते हैं। इस पहचान को बिना जांचे न लगाएं।
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यदि \(A=\{1,2\}\) और \(B=\{2,3\}\), तो \(P(A)\cup P(B)\) में कितने अवयव हैं?
If \(A=\{1,2\}\) and \(B=\{2,3\}\), how many elements are in \(P(A)\cup P(B)\)?
#sets
#power-set
#union
#inclusion-exclusion
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A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
(P(A)) and (P(B)) have \(\varnothing\) and ({2}) in common, so the total is (4+4-2=6). Remove duplicates in the union of power sets.
Step 2
Why this answer is correct
The correct answer is B. (6). (P(A)) and (P(B)) have \(\varnothing\) and ({2}) in common, so the total is (4+4-2=6). Remove duplicates in the union of power sets.
Step 3
Exam Tip
(P(A)) और (P(B)) में \(\varnothing\) तथा ({2}) समान हैं, इसलिए कुल (4+4-2=6)। पावर सेटों के संघ में दोहराव हटाएं।
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यदि \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), तो \(P(A')\cap P(A)\) क्या होगा?
If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), then what is \(P(A')\cap P(A)\)?
#sets
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#complement
#intersection
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A \(\varnothing\)
B \({\varnothing}\)
C (P(U))
D (P(A))
Explanation opens after your attempt
Correct Answer
B. \({\varnothing}\)
Step 1
Concept
(A) and (A') are disjoint, so their power sets have only \(\varnothing\) in common. Write the intersection of power sets as a set.
Step 2
Why this answer is correct
The correct answer is B. \({\varnothing}\). (A) and (A') are disjoint, so their power sets have only \(\varnothing\) in common. Write the intersection of power sets as a set.
Step 3
Exam Tip
(A) और (A') असंबद्ध हैं, इसलिए उनके पावर सेटों में केवल \(\varnothing\) समान होगा। पावर सेटों का प्रतिच्छेद एक समुच्चय के रूप में लिखें।
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यदि (U) सार्वत्रिक समुच्चय है और \(A\subseteq U\), तो \(P(A)\subseteq P(U)\) क्यों सत्य है?
If (U) is the universal set and \(A\subseteq U\), why is \(P(A)\subseteq P(U)\) true?
#sets
#power-set
#universal-set
#subset-reasoning
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A क्योंकि (A) का हर उपसमुच्चय (U) का भी उपसमुच्चय है / Because every subset of (A) is also a subset of (U)
B क्योंकि \(A\in U\) हमेशा सत्य है / Because \(A\in U\) is always true
C क्योंकि (P(A)=U) होता है / Because (P(A)=U)
D क्योंकि \(P(U)\subseteq P(A)\) होता है / Because \(P(U)\subseteq P(A)\)
Explanation opens after your attempt
Correct Answer
A. क्योंकि (A) का हर उपसमुच्चय (U) का भी उपसमुच्चय है / Because every subset of (A) is also a subset of (U)
Step 1
Concept
The universal set contains all elements of (A), so subsets of (A) are also subsets of (U). This is a basic property of power sets.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि (A) का हर उपसमुच्चय (U) का भी उपसमुच्चय है / Because every subset of (A) is also a subset of (U). The universal set contains all elements of (A), so subsets of (A) are also subsets of (U). This is a basic property of power sets.
Step 3
Exam Tip
सार्वत्रिक समुच्चय में (A) के सभी अवयव हैं, इसलिए (A) के उपसमुच्चय भी (U) के उपसमुच्चय हैं। यह पावर सेट का आधारभूत गुण है।
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यदि \(A\subseteq U\), (n(U)=7), और (n(P(A))=16), तो (n(P(A'))) क्या है?
If \(A\subseteq U\), (n(U)=7), and (n(P(A))=16), then what is (n(P(A')))?
#sets
#power-set
#universal-set
#cardinality
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A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
(n(P(A))=16=24 ), so (n(A)=4). Then (n(A')=7-4=3), and (n(P(A'))=8).
Step 2
Why this answer is correct
The correct answer is B. (8). (n(P(A))=16=24 ), so (n(A)=4). Then (n(A')=7-4=3), and (n(P(A'))=8).
Step 3
Exam Tip
(n(P(A))=16=24 ), इसलिए (n(A)=4)। तब (n(A')=7-4=3) और (n(P(A'))=8)।
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यदि (n(P(A'))=64) और (n(U)=10), तो (n(A)) क्या है?
If (n(P(A'))=64) and (n(U)=10), then what is (n(A))?
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#power-set
#complement
#reverse-counting
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A (4)
B (5)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(64=2^6\), so (n(A')=6). Since (n(U)=10), (n(A)=10-6=4).
Step 2
Why this answer is correct
The correct answer is A. (4). \(64=2^6\), so (n(A')=6). Since (n(U)=10), (n(A)=10-6=4).
Step 3
Exam Tip
\(64=2^6\), इसलिए (n(A')=6)। चूंकि (n(U)=10), इसलिए (n(A)=10-6=4)।
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किस दशा में (P(A')=P(A)) हो सकता है, जबकि पूरक (U) के सापेक्ष लिया गया है?
In which case can (P(A')=P(A)), where complement is taken with respect to (U)?
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#complement
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A जब (A=U) / When (A=U)
B जब \(A=\varnothing\) / When \(A=\varnothing\)
C जब (A=A') / When (A=A')
D जब \(A\subset U\) हमेशा / Always when \(A\subset U\)
Explanation opens after your attempt
Correct Answer
C. जब (A=A') / When (A=A')
Step 1
Concept
If power sets are equal, the original sets are equal, so (A'=A) is required. In a finite (U), this means (A) equals its complement.
Step 2
Why this answer is correct
The correct answer is C. जब (A=A') / When (A=A'). If power sets are equal, the original sets are equal, so (A'=A) is required. In a finite (U), this means (A) equals its complement.
Step 3
Exam Tip
पावर सेट बराबर हों तो मूल समुच्चय बराबर होते हैं, इसलिए (A'=A) चाहिए। सीमित (U) में यह तभी संभव है जब (A) अपने पूरक के बराबर हो।
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यदि \(A=\{1,2,3,4,5,6\}\), तो (P(A)) के कितने अवयवों में कम से कम (2) अवयव होंगे?
If \(A=\{1,2,3,4,5,6\}\), how many elements of (P(A)) have at least (2) elements?
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#power-set
#at-least
#counting
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A (56)
B (57)
C (58)
D (64)
Explanation opens after your attempt
Step 1
Concept
Total subsets are (64), and empty plus (1)-element subsets are (1+6=7). Therefore (64-7=57).
Step 2
Why this answer is correct
The correct answer is B. (57). Total subsets are (64), and empty plus (1)-element subsets are (1+6=7). Therefore (64-7=57).
Step 3
Exam Tip
कुल उपसमुच्चय (64) हैं, खाली और (1)-अवयवी उपसमुच्चय (1+6=7) हैं। अतः (64-7=57)।
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यदि \(A=\{1,2,3,4,5\}\), तो (P(A)) के कितने अवयवों में अधिकतम (2) अवयव होंगे?
If \(A=\{1,2,3,4,5\}\), how many elements of (P(A)) have at most (2) elements?
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#power-set
#at-most
#combination
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A (10)
B (15)
C (16)
D (20)
Explanation opens after your attempt
Step 1
Concept
Subsets with at most (2) elements are \(\binom{5}{0}+\binom{5}{1}+\binom{5}{2}=1+5+10=16\). For at most, add all smaller sizes.
Step 2
Why this answer is correct
The correct answer is C. (16). Subsets with at most (2) elements are \(\binom{5}{0}+\binom{5}{1}+\binom{5}{2}=1+5+10=16\). For at most, add all smaller sizes.
Step 3
Exam Tip
अधिकतम (2) अवयव वाले उपसमुच्चय \(\binom{5}{0}+\binom{5}{1}+\binom{5}{2}=1+5+10=16\) हैं। अधिकतम में सभी छोटे आकार जोड़ें।
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यदि \(A=\{a,b,c,d,e\}\), तो (P(A)) के कितने अवयव (a) और (b) दोनों को शामिल करते हैं?
If \(A=\{a,b,c,d,e\}\), how many elements of (P(A)) contain both (a) and (b)?
#sets
#power-set
#compulsory-elements
#counting
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A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
(a,b) are fixed, and the remaining (3) elements have \(2^3=8\) choices. When both are compulsory, place them first.
Step 2
Why this answer is correct
The correct answer is B. (8). (a,b) are fixed, and the remaining (3) elements have \(2^3=8\) choices. When both are compulsory, place them first.
Step 3
Exam Tip
(a,b) स्थिर हैं और शेष (3) अवयवों के \(2^3=8\) चयन हो सकते हैं। दोनों अनिवार्य हों तो उन्हें पहले रख लें।
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यदि \(A=\{a,b,c,d,e\}\), तो (P(A)) के कितने अवयव (a) या (b) में से कम से कम एक को शामिल करते हैं?
If \(A=\{a,b,c,d,e\}\), how many elements of (P(A)) contain at least one of (a) or (b)?
#sets
#power-set
#at-least-one
#counting
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A (16)
B (24)
C (28)
D (32)
Explanation opens after your attempt
Step 1
Concept
There are \(2^5=32\) total subsets, and \(2^3=8\) subsets contain neither (a) nor (b). Thus (32-8=24).
Step 2
Why this answer is correct
The correct answer is B. (24). There are \(2^5=32\) total subsets, and \(2^3=8\) subsets contain neither (a) nor (b). Thus (32-8=24).
Step 3
Exam Tip
कुल \(2^5=32\) उपसमुच्चय हैं और (a,b) दोनों न होने वाले \(2^3=8\) हैं। इसलिए (32-8=24)।
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यदि \(A=\{1,2,3,4\}\), तो (P(A)) के कितने अवयवों का योग सम है?
If \(A=\{1,2,3,4\}\), how many elements of (P(A)) have an even sum?
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#power-set
#parity
#expert-counting
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A (6)
B (8)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
For an even sum, choose an even number of odd elements from (1,3), and even elements are free, so \(2\cdot 2^2=8\). In parity questions, focus on odd elements.
Step 2
Why this answer is correct
The correct answer is B. (8). For an even sum, choose an even number of odd elements from (1,3), and even elements are free, so \(2\cdot 2^2=8\). In parity questions, focus on odd elements.
Step 3
Exam Tip
सम योग पाने के लिए विषम अवयवों (1,3) में से सम संख्या चुनी जाएगी और सम अवयव स्वतंत्र हैं, इसलिए \(2\cdot 2^2=8\)। पैरिटी में विषम अवयवों पर ध्यान दें।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\) और \(A=\{1,3,5,7\}\), तो (P(A')) के कितने अवयवों में केवल सम संख्याएँ होंगी?
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{1,3,5,7\}\), how many elements of (P(A')) contain only even numbers?
#sets
#power-set
#universal-set
#even-numbers
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A (8)
B (16)
C (32)
D (4)
Explanation opens after your attempt
Step 1
Concept
(A'={2,4,6,8}), so all its subsets contain only even numbers. The number is \(2^4=16\).
Step 2
Why this answer is correct
The correct answer is B. (16). (A'={2,4,6,8}), so all its subsets contain only even numbers. The number is \(2^4=16\).
Step 3
Exam Tip
(A'={2,4,6,8}), इसलिए इसके सभी उपसमुच्चय केवल सम संख्याओं के होंगे। संख्या \(2^4=16\) है।
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यदि \(A=\{1,2,3\}\), तो कथन \({1}\in P(A)\) और \({1}\subseteq P(A)\) में कौन सा सही है?
If \(A=\{1,2,3\}\), which is correct between \({1}\in P(A)\) and \({1}\subseteq P(A)\)?
#sets
#power-set
#element-vs-subset
#common-mistake
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A केवल \({1}\in P(A)\) सही है / Only \({1}\in P(A)\) is correct
B केवल \({1}\subseteq P(A)\) सही है / Only \({1}\subseteq P(A)\) is correct
C दोनों सही हैं / Both are correct
D दोनों गलत हैं / Both are false
Explanation opens after your attempt
Correct Answer
A. केवल \({1}\in P(A)\) सही है / Only \({1}\in P(A)\) is correct
Step 1
Concept
({1}) is a subset of (A), so it is an element of (P(A)). But (1) is not an element of (P(A)), so \({1}\subseteq P(A)\) is false.
Step 2
Why this answer is correct
The correct answer is A. केवल \({1}\in P(A)\) सही है / Only \({1}\in P(A)\) is correct. ({1}) is a subset of (A), so it is an element of (P(A)). But (1) is not an element of (P(A)), so \({1}\subseteq P(A)\) is false.
Step 3
Exam Tip
({1}) समुच्चय (A) का उपसमुच्चय है, इसलिए वह (P(A)) का अवयव है। लेकिन (1), (P(A)) का अवयव नहीं है, इसलिए \({1}\subseteq P(A)\) गलत है।
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यदि \(A=\{1,{2}\}\), तो कौन सा (P(A)) का अवयव है?
If \(A=\{1,{2}\}\), which is an element of (P(A))?
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#power-set
#nested-set
#braces
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A ({2})
B ({{2}})
C ({1,2})
D ({{1,2}})
Explanation opens after your attempt
Correct Answer
B. ({{2}})
Step 1
Concept
({2}) itself is an element of (A), so ({{2}}) is a subset of (A) and an element of (P(A)). Counting the layers is essential.
Step 2
Why this answer is correct
The correct answer is B. ({{2}}). ({2}) itself is an element of (A), so ({{2}}) is a subset of (A) and an element of (P(A)). Counting the layers is essential.
Step 3
Exam Tip
({2}) स्वयं (A) का अवयव है, इसलिए ({{2}}) (A) का उपसमुच्चय है और (P(A)) का अवयव है। परतों को गिनना जरूरी है।
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यदि \(A=\{1,2,3\}\), तो (P(A)-{\varnothing,A}) में कितने अवयव होंगे?
If \(A=\{1,2,3\}\), how many elements are in (P(A)-{\varnothing,A})?
#sets
#power-set
#set-difference
#proper-subsets
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A (4)
B (5)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(P(A)) has (8) elements, and removing \(\varnothing\) and (A) leaves (8-2=6). These are non-empty proper subsets.
Step 2
Why this answer is correct
The correct answer is C. (6). (P(A)) has (8) elements, and removing \(\varnothing\) and (A) leaves (8-2=6). These are non-empty proper subsets.
Step 3
Exam Tip
(P(A)) में (8) अवयव हैं और \(\varnothing\) तथा (A) हटाने पर (8-2=6) बचते हैं। ये गैर-रिक्त उचित उपसमुच्चय हैं।
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यदि \(U=\{1,2,3,4,5\}\), \(A=\{1,2\}\), और \(B=\{2,3,4\}\), तो (n(P(\(A\cap B\)'))) क्या है?
If \(U=\{1,2,3,4,5\}\), \(A=\{1,2\}\), and \(B=\{2,3,4\}\), then what is (n(P(\(A\cap B\)')))?
#sets
#power-set
#intersection
#complement
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A (8)
B (16)
C (32)
D (4)
Explanation opens after your attempt
Step 1
Concept
\(A\cap B={2}\), so (\(A\cap B\)'={1,3,4,5}). Its power set has \(2^4=16\) elements.
Step 2
Why this answer is correct
The correct answer is B. (16). \(A\cap B={2}\), so (\(A\cap B\)'={1,3,4,5}). Its power set has \(2^4=16\) elements.
Step 3
Exam Tip
\(A\cap B={2}\), इसलिए (\(A\cap B\)'={1,3,4,5})। इसका पावर सेट \(2^4=16\) अवयवों का होगा।
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यदि \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), और \(B=\{3,4,5\}\), तो (n(P\(A'\cup B'\))) क्या है?
If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), and \(B=\{3,4,5\}\), then what is (n(P\(A'\cup B'\)))?
#sets
#power-set
#de-morgan
#complement
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A (8)
B (16)
C (32)
D (64)
Explanation opens after your attempt
Step 1
Concept
(A'\cup B'=\(A\cap B\)'={1,2,4,5,6}), so (n(P\(A'\cup B'\))=25 =32). De Morgan's law makes counting easier.
Step 2
Why this answer is correct
The correct answer is C. (32). (A'\cup B'=\(A\cap B\)'={1,2,4,5,6}), so (n(P\(A'\cup B'\))=25 =32). De Morgan's law makes counting easier.
Step 3
Exam Tip
(A'\cup B'=\(A\cap B\)'={1,2,4,5,6}), इसलिए (n(P\(A'\cup B'\))=25 =32)। डी मॉर्गन नियम से गिनती आसान होती है।
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यदि (A) में (3) अवयव हैं, तो (P(P(P(A)))) में अवयवों की संख्या क्या है?
If (A) has (3) elements, what is the number of elements in (P(P(P(A))))?
#sets
#power-set
#nested-power-set
#expert
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A \(2^8\)
B \(2^{16}\)
C \(2^{256}\)
D (256)
Explanation opens after your attempt
Correct Answer
C. \(2^{256}\)
Step 1
Concept
(n(P(A))=23 =8), (n(P(P(A)))=28 =256), so (n(P(P(P(A))))=2^{256}). Each power set adds a new exponent.
Step 2
Why this answer is correct
The correct answer is C. \(2^{256}\). (n(P(A))=23 =8), (n(P(P(A)))=28 =256), so (n(P(P(P(A))))=2^{256}). Each power set adds a new exponent.
Step 3
Exam Tip
(n(P(A))=23 =8), (n(P(P(A)))=28 =256), इसलिए (n(P(P(P(A))))=2^{256})। हर पावर सेट पर नई घात लगती है।
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यदि \(A=\{1,2,3,4\}\), तो (P(A)) के कितने अवयवों में (1) हो या उनका आकार (2) हो?
If \(A=\{1,2,3,4\}\), how many elements of (P(A)) contain (1) or have size (2)?
#sets
#power-set
#inclusion-exclusion
#counting
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A (8)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
Subsets containing (1) are (8), and size (2) subsets are \(\binom{4}{2}=6\). Their overlap is \(\binom{3}{1}=3\), so (8+6-3=11).
Step 2
Why this answer is correct
The correct answer is C. (11). Subsets containing (1) are (8), and size (2) subsets are \(\binom{4}{2}=6\). Their overlap is \(\binom{3}{1}=3\), so (8+6-3=11).
Step 3
Exam Tip
(1) वाले उपसमुच्चय (8) हैं और आकार (2) वाले \(\binom{4}{2}=6\) हैं। दोनों में (1) और एक अन्य वाला \(\binom{3}{1}=3\) है, इसलिए (8+6-3=11)।
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यदि \(A=\{a,b,c,d\}\), तो (P(A)) के कितने अवयवों में (a) नहीं है और आकार विषम है?
If \(A=\{a,b,c,d\}\), how many elements of (P(A)) do not contain (a) and have odd size?
#sets
#power-set
#odd-subsets
#conditional-counting
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
After excluding (a), (3) elements remain, and their odd-sized subsets are \(2^{3-1}=4\). Count the size after exclusion.
Step 2
Why this answer is correct
The correct answer is C. (4). After excluding (a), (3) elements remain, and their odd-sized subsets are \(2^{3-1}=4\). Count the size after exclusion.
Step 3
Exam Tip
(a) हटाने पर (3) अवयव बचते हैं और इनके विषम आकार के उपसमुच्चय \(2^{3-1}=4\) हैं। निष्कासन के बाद ही आकार गिनें।
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यदि \(A=\{1,2,3,4,5\}\), तो (P(A)) के कितने अवयवों में (1) नहीं है और (2) अवश्य है?
If \(A=\{1,2,3,4,5\}\), how many elements of (P(A)) do not contain (1) and must contain (2)?
#sets
#power-set
#conditional-subsets
#counting
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A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
(2) is fixed and (1) is forbidden, so (3,4,5) have \(2^3=8\) choices. Handle compulsory and forbidden elements separately.
Step 2
Why this answer is correct
The correct answer is B. (8). (2) is fixed and (1) is forbidden, so (3,4,5) have \(2^3=8\) choices. Handle compulsory and forbidden elements separately.
Step 3
Exam Tip
(2) स्थिर है और (1) निषिद्ध है, इसलिए (3,4,5) के \(2^3=8\) चयन होंगे। अनिवार्य और निषिद्ध अवयव अलग-अलग संभालें।
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यदि \(A\subseteq B\), (n(A)=3), और (n(B)=5), तो (P(B)-P(A)) में कितने अवयव होंगे?
If \(A\subseteq B\), (n(A)=3), and (n(B)=5), how many elements are in (P(B)-P(A))?
#sets
#power-set
#set-difference
#subset
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A (16)
B (20)
C (24)
D (32)
Explanation opens after your attempt
Step 1
Concept
(n(P(B))=32) and (n(P(A))=8), so the difference has (32-8=24) elements. Since \(A\subseteq B\), \(P(A)\subseteq P(B)\).
Step 2
Why this answer is correct
The correct answer is C. (24). (n(P(B))=32) and (n(P(A))=8), so the difference has (32-8=24) elements. Since \(A\subseteq B\), \(P(A)\subseteq P(B)\).
Step 3
Exam Tip
(n(P(B))=32) और (n(P(A))=8), इसलिए अंतर में (32-8=24) अवयव हैं। \(A\subseteq B\) होने से \(P(A)\subseteq P(B)\) है।
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यदि \(U=\{1,2,3,4,5,6,7\}\) और \(A=\{2,4,6\}\), तो (P(A')) के कितने अवयवों में (1) और (7) दोनों होंगे?
If \(U=\{1,2,3,4,5,6,7\}\) and \(A=\{2,4,6\}\), how many elements of (P(A')) contain both (1) and (7)?
#sets
#power-set
#complement
#compulsory-elements
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A (2)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
(A'={1,3,5,7}). Fixing (1,7), the elements (3,5) have \(2^2=4\) choices.
Step 2
Why this answer is correct
The correct answer is B. (4). (A'={1,3,5,7}). Fixing (1,7), the elements (3,5) have \(2^2=4\) choices.
Step 3
Exam Tip
(A'={1,3,5,7}) है। (1,7) स्थिर रखने पर (3,5) के \(2^2=4\) चयन होंगे।
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यदि \(A=\{1,2,3,4\}\), तो (P(A)) के उन अवयवों की संख्या क्या है जो (A) से असंबद्ध हैं?
If \(A=\{1,2,3,4\}\), what is the number of elements of (P(A)) that are disjoint from (A)?
#sets
#power-set
#disjoint-set
#concept
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A (0)
B (1)
C (4)
D (16)
Explanation opens after your attempt
Step 1
Concept
Only the subset \(\varnothing\) of (A) is disjoint from (A). Therefore the number is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). Only the subset \(\varnothing\) of (A) is disjoint from (A). Therefore the number is (1).
Step 3
Exam Tip
(A) का केवल \(\varnothing\) उपसमुच्चय ही (A) से असंबद्ध होता है। इसलिए संख्या (1) है।
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