Sets and Relations

Let $A$ and $B$ be two sets such that $A\cap\,X=B\cap\,X=\varphi\,$ and $A\cup\,X=B\cup\,X$ for same set $X$. Then,

In a statistical investigation of 1003 families of Calcutta, it was found that 63 families has neither a radio nor a TV, 794 families has a radio and 187 has TV. The number of families in that group having both a radio…

Let $R$ be the relation "is congruent to" on the set of all triangles in a plane is

Number of subsets of set of letter of word 'MONOTONE'.

If $n(\mathrm{~A})=1000, n(\mathrm{~B})=500$ and if $n(\mathrm{~A} \cap \mathrm{B}) \geq 1$ and $n(\mathrm{~A} \cup \mathrm{B})=p$, then

A set $A$ has 3 elements and another set B has 6 elements. Then

If $A=\{x: x$ is a multiple of 4$\}$ and, $B=\{x: x$ is a multiple of 6$\}$, then $A \cap B$ consists of multiples of

Let $A$ and $B$ be two sets such that $A∩X=B∩X=ϕ$ and $A∪X=B∪X$ for same set $X$. Then,

Let $A=\{1, 2, 3, 4, 5\}$ and $R$ be a relation defined by $R=\{(x, y):x, y∈A, x+y=5\}$. Then, $R$ is

Two finite sets have $m$ and $n$ elements. The number of subsets of the first set is 112 more than that of the second set. The values of $m$ and $n$ respectively are,

If $\rho=\left\{(x, y) \mid x^{2}+y^{2}=1 ; x, y \in \mathbb{R}\right\}$. Then, $\rho$ is

Universal set, $U=\left\{x \mid x^{5}-6 x^{4}+11 x^{3}-6 x^{2}=0\right\}$ $A=\left\{x \mid x^{2}-5 x+6=0\right\}$ $\mathrm{B}=\left\{\mathrm{x} \mid \mathrm{x}^{2}-3\mathrm{x}+2=0\right\}$ What is $(A \cap B)^{\prime}$…