Question

Let $ A $ and $ B $ be finite sets such that $ n(A) = 3 $ . If the total number of relations that can be defined from $ A $ to $ B $ is $ 4096 $ , then $ n(B) = $

• A. $ 5 $
• B. $ 4 $
• C. $ 6 $
• D. $ 8 $

Answer 1

Answer: (B)

Let the number of elements in set $B$ be $x$.
Number of elements in set $A = 3$
Number of relations from $A$ to $B = 4096$
$\Rightarrow 2^{3x} = 4096$
$\Rightarrow 2^{3x} = 2^{12}$
On comparing, we get $3x = 12 \Rightarrow x = 4$
So, number of elements in set $B = 4$