Let a set A = A₁ A₂..... A k, where A i A j = φ for i ≠ j, 1 ≤ j, j ≤ k. Define the relation R from A to A by R = (x, y): y A i if and only if x A i, 1 ≤ i ≤ k. Then, R is:

(A) reflexive, symmetric but not transitive.

(B) reflexive, transitive but not symmetric.

(C) reflexive but not symmetric and transitive.

Sets, Relations and Functions: JEE Main 2022 Mathematics question

JEE Main 2022 · 29 Jun, Morning shift · Q5380

JEE Main 202229 Jun, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let a set A = A₁

\cup

A₂

\cup

.....

\cup

A_k, where A_i

\cap

A_j =

\phi

for i

\ne

j, 1

\le

j, j

\le

k. Define the relation R from A to A by R = {(x, y) : y

\in

A_i if and only if x

\in

A_i, 1

\le

\le

k}. Then, R is :