Two finite sets $X$ and $Y$ have $p$ and $q$ elements respectively. If the total number of subsets o

Question

Two finite sets $X$ and $Y$ have $p$ and $q$ elements respectively. If the total number of subsets of $X$ is 56 more than the total number of subsets of $Y$. Then the value of $q$ is

Professor PC Thomas Classes · Answer

$2^p - 2^q = 56 \Rightarrow 2^3(2^{p-3} - 1) = 8 	imes 7 \Rightarrow 2^q = 2^3 \Rightarrow q=3$.