Question

Let $A=\{p, q, r\}$. Which of the following is an equivalence relation on A?

(A) $R_1=\{(p, q),(q, r),(p, r)(p, p)\}$

(B) $R_2=\{(r, q),(r, p),(r, r)(q, q)\}$

(C) $R_3=\{(p, p),(q, q),(r, r)(p, q)\}$

(D) none of these

Answer 1

$(A)(q, q) \notin R_1$, Not reflexive

$(B) (p, p) \propto R_2$, not reflexive

$(C) (q, p) \propto R_3$, not symmetric

Above Correct Answer is Option B.