EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 1 February 2023 Shift 1>Q 50

HARD

JEE Main

IMPORTANT

Earn 100

Let $R$ be a relation on $ℝ$ , given by $R = {(a, b) : 3 a - 3 b + \sqrt{7}$ is an irrational number $}$ . Then $R$ is

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Important Questions on Set Theory and Relations

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 1 February 2023 Shift 2>Q 51

Let

P (S)

denote the power set of

S = \{1, 2, 3, \dots, 10\}

. Define the relations

R_{1}

and

R_{2}

on

P (S)

as

A R_{1} B

if

(A \cap B^{c}) \cup (B \cap A^{c}) = ϕ

and

A R_{2} B

if

A \cup B^{c} = B \cup A^{c}, \forall A, B \in P (S)

. Then :