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:

• A. $3^5$
• B. $5^2$
• C. $2^5$
• D. $5^3$

Answer 1

The correct option is A $3^5$

Every element in set $X$ has 3 options. Element can go to either set $Y$ or set $Z$ or none of these sets.

For each element , there are 3 options.
So 5 elements in set $X$ has $3^5$ options.

$\therefore$ Total number of ordered pairs $=3^5$