The set expression $A \cup\left(B \cap\left(A^{\prime} \cup B^{\prime}\right)\right)$ is equivalent to

The relation $R=\{(1,1),(2,2),(3,3)\}$ on the set $\{1,2,3\}$ is

Two finite sets have $m$ and $n$ elements. The total number of proper subsets of the first set is 119 more than the total number of subsets of the second set. Find the value of $m-n$

If $P=\{5 m: m \in N\}$ and $Q=\left\{5^m: m \in N\right\}$, where $N$ is set of natural numbers, then