Let A = {p, q, r}. Which of the following is | vedclass

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(D) An equivalence relation on a set $A$ must be reflexive,symmetric,and transitive.For a relation to be reflexive,for every $x \in A$,$(x, x)$ must b

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None of these

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(D) An equivalence relation on a set $A$ must be reflexive,symmetric,and transitive.For a relation to be reflexive,for every $x \in A$,$(x, x)$ must be in the relation.Here,$A = \{p, q, r\}$. Thus,$(p, p), (q, q),$ and $(r, r)$ must all be present in the relation.$1$. In $R_1$,$(q, q)$ and $(r, r)$ are missing. Thus,$R_1$ is not reflexive.$2$. In $R_2$,$(p, p)$ is missing. Thus,$R_2$ is not reflexive.$3$. In $R_3$,$(r, r)$ is present,but $(p, p)$ and $(q, q)$ are present,however,$(r, r)$ is present but it is not symmetric because $(p, q) \in R_3$ but $(q, p) 
otin R_3$.Since none of the given relations satisfy the conditions of reflexivity,symmetry,and transitivity,none of them are equivalence relations.Therefore,all the given options $R_1, R_2,$ and $R_3$ are not equivalence relations. However,the question asks which is $NOT$ an equivalence relation,and since all are not,the most appropriate answer is that none of the provided sets form an equivalence relation.

Let $A = \{p, q, r\}$. Which of the following is $NOT$ an equivalence relation on $A$?

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