If A=a,b,c,d then a relation R=(a,b),(b,a),(a,a) on A is(A) Reflexive…

The correct answer is Option (4) → (B) only

R = {(a, b), (b, a), (a, a)} on A = {a, b, c, d}.

Reflexive needs (x, x) for every element of A, but (b, b), (c, c) and (d, d) are not in R.

Every pair has its reverse in R: (a, b) and (b, a) are both in R, and (a, a) is its own reverse.

For transitivity, (b, a) ∈ R and (a, b) ∈ R would need (b, b) ∈ R, which is missing.

So R is symmetric, but neither reflexive nor transitive.

Checking the statements

(A) Reflexive — Incorrect. (b, b), (c, c) and (d, d) are not in R.

(B) Symmetric — Correct. (a, b) and (b, a) are both in R.

(C) Transitive — Incorrect. (b, a), (a, b) ∈ R but (b, b) ∉ R.

(D) Symmetric and transitive — Incorrect. R is not transitive, since (b, b) ∉ R.