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(D) relation $R$ on a set $A$ is called an equivalence relation if and only if it satisfies the following three properties:$1$. Reflexive: For every $

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Possesses all the above three properties

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(D) relation $R$ on a set $A$ is called an equivalence relation if and only if it satisfies the following three properties:$1$. Reflexive: For every $a \in A$,$(a, a) \in R$.$2$. Symmetric: If $(a, b) \in R$,then $(b, a) \in R$ for all $a, b \in A$.$3$. Transitive: If $(a, b) \in R$ and $(b, c) \in R$,then $(a, c) \in R$ for all $a, b, c \in A$.Since an equivalence relation must satisfy all three conditions,option $D$ is the correct answer.

In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation,it is sufficient,if $R$

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