Let X, Y, Z be sets of sizes x, y and z respectively. Let W = X x Y. Let E be…

Key steps:

• Compute the size of W = X × Y: |W| = x * y.

• The set E is the power set of W, so |E| = 2^{x y}.

• The number of functions from a set of size z to a set of size 2^{x y} is (2^{x y})^{z} = 2^{x y z}.

Answer: 2^{x y z}