Relation S = {(3,3), (4,4)} on set A = {3, 4, | vedclass

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(A) For a relation $S$ on set $A = \{3, 4, 5\}$ to be reflexive,$(a, a)$ must be in $S$ for all $a \in A$. Here,$(5, 5) 
otin S$,so it is not reflexi

Vedclass · Accepted Answer

symmetric and transitive but not reflexive

Vedclass · Answer

(A) For a relation $S$ on set $A = \{3, 4, 5\}$ to be reflexive,$(a, a)$ must be in $S$ for all $a \in A$. Here,$(5, 5) 
otin S$,so it is not reflexive.For $S$ to be symmetric,if $(a, b) \in S$,then $(b, a) \in S$. Since $(3, 3)$ and $(4, 4)$ are in $S$,their reverses are also in $S$. Thus,it is symmetric.For $S$ to be transitive,if $(a, b) \in S$ and $(b, c) \in S$,then $(a, c) \in S$. For $(3, 3)$ and $(3, 3)$,$(3, 3) \in S$. Similarly for $(4, 4)$. Thus,it is transitive.Therefore,the relation is symmetric and transitive but not reflexive.

Relation $S = \{(3,3), (4,4)\}$ on set $A = \{3, 4, 5\}$ is . . . . . . .

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