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यदि \(A=\{1,2,4\}\) और \(B=\{1,4,16\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि \(y=x^2\)?
If \(A=\{1,2,4\}\) and \(B=\{1,4,16\}\), how many pairs ((x,y)) in \(A\times B\) satisfy \(y=x^2\)?
#cartesian-product
#relation
#function-condition
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A (2)
B (3)
C (4)
D (6)
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Step 1
Concept
The valid pairs are ((1,1),(2,4),(4,16)). Applying a condition to a Cartesian product forms a relation.
Step 2
Why this answer is correct
The correct answer is B. (3). The valid pairs are ((1,1),(2,4),(4,16)). Applying a condition to a Cartesian product forms a relation.
Step 3
Exam Tip
सही युग्म ((1,1),(2,4),(4,16)) हैं। कार्तीय गुणन पर शर्त लगाने से संबंध बनता है।
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यदि \(A=\{1,2\}\) और \(B=\{5,6,7\}\) हैं, तो (A) से (B) तक कुल कितने संबंध संभव हैं?
If \(A=\{1,2\}\) and \(B=\{5,6,7\}\), how many relations are possible from (A) to (B)?
#cartesian-product
#relations
#subsets
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A (6)
B \(2^5\)
C \(2^6\)
D \(3^2\)
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Correct Answer
C. \(2^6\)
Step 1
Concept
(n\(A\times B\)=2\times3=6), and every relation is a subset of \(A\times B\). Therefore the total number of relations is \(2^6\).
Step 2
Why this answer is correct
The correct answer is C. \(2^6\). (n\(A\times B\)=2\times3=6), and every relation is a subset of \(A\times B\). Therefore the total number of relations is \(2^6\).
Step 3
Exam Tip
(n\(A\times B\)=2\times3=6), और हर संबंध \(A\times B\) का उपसमुच्चय होता है। इसलिए कुल संबंध \(2^6\) हैं।
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यदि \(A=\{2,4,6\}\) और \(B=\{1,3\}\) हैं, तो कौन सा उपसमुच्चय (A) से (B) तक संबंध है?
If \(A=\{2,4,6\}\) and \(B=\{1,3\}\), which subset is a relation from (A) to (B)?
#cartesian-product
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#subset
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A ({(2,1),(6,3)})
B ({(1,2),(3,6)})
C ({(4,5)})
D ({(0,1),(2,3)})
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Correct Answer
A. ({(2,1),(6,3)})
Step 1
Concept
A relation is a subset of \(A\times B\). Only all pairs of ({(2,1),(6,3)}) belong to \(A\times B\).
Step 2
Why this answer is correct
The correct answer is A. ({(2,1),(6,3)}). A relation is a subset of \(A\times B\). Only all pairs of ({(2,1),(6,3)}) belong to \(A\times B\).
Step 3
Exam Tip
संबंध \(A\times B\) का उपसमुच्चय होता है। केवल ({(2,1),(6,3)}) के सभी युग्म \(A\times B\) में हैं।
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\(यदि (A={1,2,3,4}), (B={a,b}) और (R={(x,y):x\in A,,y\in B,,x\) सम है}) है, तो कौन सा युग्म (R) में होगा?
\(If (A={1,2,3,4}), (B={a,b}) and (R={(x,y):x\in A,,y\in B,,x\) is even}), which pair belongs to (R)?
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A ((1,a))
B ((a,2))
C ((4,b))
D ((3,b))
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Correct Answer
C. ((4,b))
Step 1
Concept
\(4\in A\) is even and \(b\in B\), so \((4,b)\in R\). Apply the relation condition to every option.
Step 2
Why this answer is correct
The correct answer is C. ((4,b)). \(4\in A\) is even and \(b\in B\), so \((4,b)\in R\). Apply the relation condition to every option.
Step 3
Exam Tip
\(4\in A\) सम है और \(b\in B\), इसलिए \((4,b)\in R\)। संबंध की शर्त को हर विकल्प पर लगाएं।
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यदि \(A=\{0,1,2\}\), \(B=\{3,4\}\) और \(R=\{(0,3),(2,4)\}\) है, तो (R) किसका उपसमुच्चय है?
If \(A=\{0,1,2\}\), \(B=\{3,4\}\) and \(R=\{(0,3),(2,4)\}\), then (R) is a subset of which set?
#cartesian-product
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A \(B\times A\)
B \(A\cap B\)
C \(A\times B\)
D \(A\cup B\)
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Correct Answer
C. \(A\times B\)
Step 1
Concept
In every pair of (R), the first component is from (A) and the second is from (B). Therefore \(R\subseteq A\times B\).
Step 2
Why this answer is correct
The correct answer is C. \(A\times B\). In every pair of (R), the first component is from (A) and the second is from (B). Therefore \(R\subseteq A\times B\).
Step 3
Exam Tip
(R) के हर युग्म में पहला घटक (A) से और दूसरा (B) से है। इसलिए \(R\subseteq A\times B\)।
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