For the set A = {1, 2, 3},consider the relati | vedclass

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(A) $1$. Reflexivity: $A$ relation $S$ is reflexive if $(a, a) \in S$ for all $a \in A$. Here,$(1, 1) 
otin S$,so $S$ is not reflexive.$2$. Symmetry:

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not transitive

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(A) $1$. Reflexivity: $A$ relation $S$ is reflexive if $(a, a) \in S$ for all $a \in A$. Here,$(1, 1) 
otin S$,so $S$ is not reflexive.$2$. Symmetry: $A$ relation $S$ is symmetric if $(a, b) \in S \implies (b, a) \in S$. Here,$(1, 2) \in S$ but $(2, 1) \in S$ (True),and $(2, 3) \in S$ but $(3, 2) 
otin S$. Since $(3, 2) 
otin S$,the relation is not symmetric.$3$. Transitivity: $A$ relation $S$ is transitive if $(a, b) \in S$ and $(b, c) \in S \implies (a, c) \in S$. Here,$(1, 2) \in S$ and $(2, 3) \in S$,but $(1, 3) 
otin S$. Therefore,the relation is not transitive.$4$. Conclusion: Since $S$ is not reflexive,not symmetric,and not transitive,the correct description is that it is not transitive. Thus,option $A$ is correct.

For the set $A = \{1, 2, 3\}$,consider the relation $S = \{(1, 2), (2, 1), (2, 3)\}$ on $A$. Then,the relation $S$ is . . . . . . .

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