Let R = {(3, 3), (5, 5), (9, 9), (12, 12), (5 | vedclass

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(D) Given the set $A = \{3, 5, 9, 12\}$ and the relation $R = \{(3, 3), (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)\}$.$1$. Reflexivity

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reflexive,transitive but not symmetric.

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(D) Given the set $A = \{3, 5, 9, 12\}$ and the relation $R = \{(3, 3), (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)\}$.$1$. Reflexivity: For $R$ to be reflexive,$(a, a) \in R$ for all $a \in A$. Since $(3, 3), (5, 5), (9, 9), (12, 12) \in R$,the relation is reflexive.$2$. Symmetry: For $R$ to be symmetric,if $(a, b) \in R$,then $(b, a) \in R$. Here,$(3, 5) \in R$,but $(5, 3) 
otin R$. Thus,$R$ is not symmetric.$3$. Transitivity: For $R$ to be transitive,if $(a, b) \in R$ and $(b, c) \in R$,then $(a, c) \in R$. Checking the pairs: $(3, 5) \in R$ and $(5, 12) \in R$,we must have $(3, 12) \in R$,which is present. Checking other combinations,the property holds for all elements. Thus,$R$ is transitive.Therefore,$R$ is reflexive and transitive but not symmetric.

Let $R = \{(3, 3), (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)\}$ be a relation on the set $A = \{3, 5, 9, 12\}.$ Then,$R$ is

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