Question

Let, X,Y,Z be sets of sizes x,y and z respectively.
Let W = X $\times$ Y and E be the set of the all subsets of W. The number of functions from Z to E is

• A. z
• B. z$\times$$2^{xy}$
• C. $2^z$
• D. 2${}^{xyz}$

Answer 1

The correct option is D 2${}^{xyz}$

Given |X| = x, |Y| = y and |Z| = z
W = X $\times$ Y
So |W| = xy
|E| = 2${}^{|w|}$ = 2${}^{xy}$
So the number of functions for Z to E = |E|${}^{|z|}$
= (2${}^{xy}$)${}^z$ =2${}^{xyz}$