# GATE Questions & Answers of Sets

## What is the Weightage of Sets in GATE Exam?

Total 3 Questions have been asked from Sets topic of Discrete Mathematics subject in previous GATE papers. Average marks 1.00.

Let $U=\{1,2,\;...\;,\;n\}.$ Let $A=\{(x,\;X)\;\vert x\in X,\;X\subseteq U\}.$ Consider the following two statements on |A|.

I.  $\vert A\vert=n2^{n-1}$

II. $\vert A\vert={\textstyle\sum_{k=1}^n}k\begin{pmatrix}n\\k\end{pmatrix}$

Which of the above statements is/are TRUE?

Let $G$ be an arbitrary group. Consider the following relations on $G$:

$R_1:\forall a,\;b\in G,\;a\;R_1b$ if and only if $\exists g\in G$ such that $a=g^{-1}bg$

$R_2:\forall a,\;b\in G,\;a\;R_2b$ if and only if $a=b^{-1}$

Which of the above is/are equivalence relation/relations?

A binary operation $\oplus$ on a set of integers is defined as $x\oplus y={x}^{2}+{y}^{2}$ . Which one of the following statements is TRUE about $\oplus$?