R is reflexive and symmetric but not transitive.

R is reflexive and transitive but not symmetric.

R is symmetric and transitive but not reflexive.

R is an equivalence relation.

solution:

Leave R alone the connection in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3),

(3, 2)}.

Stage 1: (1, 1), (2, 2), (3, 3), (4, 4) ∈ R R. R is reflexive.

Stage 2: (1, 2) ∈ R yet (2, 1) ∉ R. R isn’t symmetric.

Stage 3: Consider any arrangement of focuses, (1, 3) ∈ R and (3, 2) ∈ R then, at that point (1, 2) ∈ R. So R is transitive.

Alternative (B) is right.