Embibe Experts Solutions for Chapter: Set Theory and Relations, Exercise 1: JKCET 2017

$A$ set $T$ is given as $T=\left\{x\in R\mid (x-3)=(x+4{)}^2,x<2\right\}.$ Which of these would be TRUE about the set $T ?$

If $A$ and $B$ are two non-empty finite sets having $3$ and $4$ elements respectively, then what would be the possible number of subsets of $A\times B?$

There is a set $P$ of ordered pairs in which each pair has a vowel as first element and a consonant as second element. It is given that $M=4^{10}.$ How many elements will be there in power set of $P$ ?

Two sets $A$ and $B$ have $27$ and $33$ elements respectively. If $(A\cup B)$ contains $48$ elements, then how many elements are there in $(A\cap B)?$

If $n\left(P\right)=8, n\left(Q\right)=10$ and $n\left(R\right)=5$ ($\text{'}n\text{'}$ denotes cardinality) for three disjoint sets $P, Q, R$, then $n\left(PUQUR\right)=$

If there are $2$ elements in a set $A,$ then what would be the number of possible relations from the set $A$ to set $A?$

If $A$ and $B$ are two non-empty finite sets having $3$ and $4$ elements respectively, then what would be the number of ordered pairs in $A\times B?$

Suppose $P, Q$ and $R$ are three sets, each with three elements. The number of subsets of the set $P\times Q\times R,$ that have at least $2$ elements is