Question

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

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

Answer 1

The correct option is B $3^5$

Let X = {1, 2, 3, 4, 5}
Total no. of elements = 5
Each elements has 3 options. Either set Y or set Z or none. $(\because Y\cap Z=\varphi )$
So, number of ordered pairs $=3^5$