Let R = {(a, a)} be a relation on a set A. Th | vedclass

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(C) relation $R$ on a set $A$ is symmetric if $(x, y) \in R \implies (y, x) \in R$ for all $x, y \in A$. Here,$R = \{(a, a)\}$. Since $(a, a) \in R$,i

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Symmetric and anti-symmetric

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(C) relation $R$ on a set $A$ is symmetric if $(x, y) \in R \implies (y, x) \in R$ for all $x, y \in A$. Here,$R = \{(a, a)\}$. Since $(a, a) \in R$,its reverse $(a, a)$ is also in $R$. Thus,$R$ is symmetric.$A$ relation $R$ on a set $A$ is anti-symmetric if $(x, y) \in R$ and $(y, x) \in R \implies x = y$ for all $x, y \in A$. Here,$(a, a) \in R$ and $(a, a) \in R$ implies $a = a$,which is true. Thus,$R$ is anti-symmetric.Therefore,$R$ is both symmetric and anti-symmetric.

Let $R = \{(a, a)\}$ be a relation on a set $A$. Then $R$ is:

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