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 on a set of integers is defined as x y = x 2 + y 2 . Which one of the following statements is TRUE about ?