Let Consider,
I am assigning A to myself, B to my beautiful friend , and You are C.
Then $(P,Q)$ means P is friend of Q.
Then,
She is my friend means I am friend of her i.e. (A,B).
You are her friend means (C,B).
We are friend means I am your friend i.e. (A, C)
Now Relation R = { (A,B), (C,B), (A,C) }
This relation has (A,B) but does not have (B,A) hence its can not be commutative.
Since its is not commutative, hence it can not be equivalence.
Its Transitive, because set has (A.C), (C, B) and also has (A,B).
And its not Implicative also.
But there in no option only for transitivity. Hence answer will be D) None of the above