Let $$R = \{(1, 2), (3, 4), (2, 2)\}$$​ and
$$S = \{(4, 2), (2, 5), (3, 1), (1, 3)\}$$​ be two relations. The composite relation $$R \circ S$$​ of $$R$$​ and S is:

Correct option is B

We are given two relations:
R = {(1,2), (3,4), (2,2)}
and
S = {(4,2), (2,5), (3,1), (1,3)}
For this question, the composition R ∘ S is being taken as:
R ∘ S = {(a, c) : (a, b) ∈ R and (b, c) ∈ S}
In other words, the second element of a pair in R must match the first element of a pair in S.
Step 1: Consider (1, 2) ∈ R
We need a pair in S beginning with 2.
(2, 5) ∈ S
Therefore:
(1,2), (2,5) => (1,5)
So, (1,5)
Step 2: Consider (3, 4) ∈ R
We need a pair in S beginning with 4.
(4, 2) ∈ S
Therefore:
(3,4), (4,2) => (3,2)
So, (3,2)
Step 3: Consider (2,2) ∈ R
Again, we need a pair in S beginning with 2:
(2,5) ∈ S
Therefore:
(2,2), (2,5) => (2,5)
So, (2,5)
Therefore,
R∘S = {(1,5), (3,2), (2,5)}
Hence,
(b) {(1,5), (3,2), (2,5)}