If a set $A$ has 5 elements, then the number of ways of selecting two subsets $P$ and $Q$ from $A$ such that…
If a set $A$ has 5 elements, then the number of ways of selecting two subsets $P$ and $Q$ from $A$ such that $P$ and $Q$ are mutually disjoint, is
$64$
$128$
$243$
$729$
Solution
Given set A has 5 elements, there are two subsets $P$ and Q which are mutually disjoint. So, the required number of ways of selecting two subsets will be $3^5=243$.