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 total number of subsets of W.
Now, the mapping for a function from A to B with N and M elements respectively... we have $M^{N}$^{ }.
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}
Gatecse