JEE Main 2022 · 29 Jun · Shift 1 · Mathematics Q11

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MathematicsSingle correct+4 / -1Question 11 of 90

Let a set $A=A_1\cup A_2\cup\dots\cup A_k$ , where $A_i\cap A_j=\phi$ for $i\ne j$ , $1\le i,j\le k$ . Define the relation R from A to A by $R=\{(x,y):y\in A_i\text{ if and only if }x\in A_i,\ 1\le i\le k\}$ . Then, R is :

reflexive, symmetric but not transitive

reflexive, transitive but not symmetric

reflexive but not symmetric and transitive

an equivalence relation

Answer and worked solution

Official answer: D

R relates two elements exactly when they lie in the same block of the partition: reflexive, symmetric and transitive.

(D)

Topics:Relations

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JEE Main 2022 · 29 Jun · Shift 1, Mathematics question 11