Let A = {a, b, c, d} and B = {4, 8, 16, 32). If the total number of relations from A to B is $2^{x}$ find the value of $\frac{(x)}{2}$ ?

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Solution

Total number of relations that can be defined from set A to a set B is the number of possible subset of A $\times$ B.

n(A $\times$ B) = 4 $\times$ 4 = 16

Total number of relations = $2^{16}$

x = 16

$\frac{x}{2}$ = 8

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