First slide

Introduction to Relations (XI) on Sets

Question

Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that
$Y \subseteq X, Z \subseteq X$ and $Y \cap Z$ is empty is

Moderate

A

$2^{5}$
B

$5^{3}$
C

$5^{2}$
D

$3^{5}$

Solution

For each $x \in X$ , we have three choices 5
$x \in Y,$ $x \notin Z,$ $x \in Z; x \notin Y, x \notin Z$
So the required number of ordered pairs is 3⁵

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