Multiple choice

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

  1. $z^{2^{xy}}$
  2. $z \times 2^{xy}$
  3. $z^{2^{x+y}}$
  4. $2^{xyz}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The number of functions from a set A to a set B Where, |A | = m and, |B| = n is nm Also W = X x Y $\Rightarrow$| W | = xy $\because$| E | = 2xy |Z| = z So, the number of functions from Z to E is (2xy)z = 2xyz

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