Embibe Experts Solutions for Chapter: Set Theory and Relations, Exercise 1: AMU-AT (B.Tech.) 2017

An investigator interviewed $100$ students to determine the performance of three drinks milk, coffee and tea. The investigator reported that $10$ students take all three drinks milk, coffee and tea; $20$ students take milk and coffee, $30$ students take coffee and tea, $25$ students take milk and tea, $12$ students take milk only, $5$ students take coffee only and $8$ students take tea only. Then the number of students who did not take any of the three drinks is

Let $Y=\left\{1,2,3,4,5\right\}, A=\left\{1,2\right\}, B=\left\{3,4,5\right\}$ and $\varphi$ denotes null set. If $\left(A\times B\right)$ denotes cartesian product of the sets $A$ and $B$, then $\left(Y\times A\right)\cap \left(Y\times B\right)$ is

Let $A=\left\{2,3,4,5,\dots .,16,17,18\right\}.$ Let $\approx$ be the equivalence relation on $A\times A$ cartesian product of $A$ and $A$, defined by $\left(a,b\right)\approx \left(c,d\right)$ if $ad=bc,$ then the number of ordered pairs of the equivalence class of $(3,2)$ is

Let $R$ and $S$ be any two equivalence relations on a set $X$. Then which of the following is incorrect statement

Consider the following relations in the real numbers $R_1=\left\{(x,y)\mid x^2+y^2\le 25\right\}$ and $R_2=\left\{(x,y),y\ge \frac{4x^2}{9}\right\}$, then the range of $R_1\cap R_2$ is

If $A$ and $B$ are disjoint sets, then $B\cap A^{\text{'}}$, where $A^{\text{'}}$ is complement of $A$, is equal to

For any three sets $A, B$ and $C$ the set $(A\cup B\cup C)\cap {\left(A\cap B^{\text{'}}\cap C^{\text{'}}\right)}^{\text{'}}\cap C^{\text{'}}$ is equal to