If a relation R on the set {1, 2, 3} is defin | vedclass

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Question

(C) Let $A = \{1, 2, 3\}$.For $R$ to be reflexive,$(a, a) \in R$ for all $a \in A$. Since $(2, 2) 
otin R$ and $(3, 3) 
otin R$,$R$ is not reflexive

Vedclass · Accepted Answer

Symmetric and transitive

Vedclass · Answer

(C) Let $A = \{1, 2, 3\}$.For $R$ to be reflexive,$(a, a) \in R$ for all $a \in A$. Since $(2, 2) 
otin R$ and $(3, 3) 
otin R$,$R$ is not reflexive.For $R$ to be symmetric,if $(a, b) \in R$,then $(b, a) \in R$. Here,$(1, 1) \in R$ implies $(1, 1) \in R$,which holds true. Thus,$R$ is symmetric.For $R$ to be transitive,if $(a, b) \in R$ and $(b, c) \in R$,then $(a, c) \in R$. Since there is only one element $(1, 1)$,the condition holds vacuously. Thus,$R$ is transitive.Therefore,$R$ is symmetric and transitive.

If a relation $R$ on the set $\{1, 2, 3\}$ is defined by $R = \{(1, 1)\}$,then $R$ is

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