Let $X,Y,Z$ be sets of sizes $x, y$ and $z$ respectively. Let $W = X \times Y$ and $E$ be the set of all subsets of $W$. The number of functions from $Z$ to $E$ is
D is Correct.
$|E| = 2^{xy}$ which is the number of subsets of $W.$
Now, the mapping for a function from $A$ to $B$ with $N$ and $M$ elements respectively can be done in $M^{N}$^{ }ways.
Here,
$|E|^z = \{2^{xy}\}^z = 2^{xyz}$
W = X ⨉ Y ,∣ W ∣ = xy
E = powerset of ( X ⨉ Y ) , ∣ E ∣ = 2^{xy}
Let f be the function , f : Z ---> E
Total number of functions from Z ---> E = ∣ E ∣^{ ∣ Z ∣ }= 2^{xyz}