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Number of Relations from Even to Prime Sets | JEE Sets

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Question
If AA is the set of even natural numbers less than 88 and BB is the set of prime numbers less than 77, then the number of relations from AA to BB is:
A292^9correct
B929^2
C323^2
D29−12^{9}-1
Solution
A={2,4,6},B={2,3,5}⇒n(A×B)=3×3=9.A = \{2, 4, 6\}, \quad B = \{2, 3, 5\} \Rightarrow n(A \times B) = 3 \times 3 = 9.
 A relation is any subset of A×BA \times B, so
number of relations=2n(A×B)=29.\text{number of relations} = 2^{n(A \times B)} = 2^9.
 Correct answer: (1)
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