If R and R' are symmetric relations (not disjoint) on a set A, then t…

Since R ∩ R' are not disjoint, there is at least one ordered pair, say, (a, b) in R ∩ R'.

but (a, b) ∈ R ∩ R' ⇒ (a, b) ∈ R and (a, b) ∈ R'

since R and R' are symmetric relations, we get

(b, a) ∈ R and (b, a) ∈ R'

and consequently (b, a) ∈ R ∩ R'

similarly if any other ordered pair (c, d) ∈ R ∩ R', then we must also have,

(d, c) ∈ R ∩ R'

hence R ∩ R' is symmetric.

Hence (2) is the correct answer.