Embibe Experts Solutions for Chapter: Set Theory and Relations, Exercise 1: KCET (UG) 2021

If $U$ is the universal set with $100$ elements; $A$ and $B$ are two sets such that $n\left(A\right)=50, n\left(B\right)=60$ $n\left(A\cap B\right)=20$ then $n\left(A^{\text{'}}\cap B^{\text{'}}\right)=$

In a certain town $65\%$ families own cell phones, $15000$ families own scooter and $15\%$ families own both. Taking into consideration that the families own at least one of the two, the total number of families in the town is

If $n\left(A\right)=2$ and total number of possible relations from set $A$ to set $B$ is $1024$, then $n\left(B\right)$ is

$A$ and $B$ are non-singleton sets and $n\left(A\times B\right)=35$. If $B\subset A$, then ${}^{n\left(A\right)}C_{n\left(B\right)}=$

If a relation $R$ on  the set $\left\{1,2,3\right\}$ be defined by $R=\left\{\left(1,1\right)\right\}$, then $R$ is