A relation R defined on the set A = {a, b, c} | vedclass

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(B) To determine the properties of the relation $R$ on set $A = \{a, b, c\}$:$1$. Reflexivity: For a relation to be reflexive,$(x, x) \in R$ for all $

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reflexive and transitive but not symmetric.

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(B) To determine the properties of the relation $R$ on set $A = \{a, b, c\}$:$1$. Reflexivity: For a relation to be reflexive,$(x, x) \in R$ for all $x \in A$. Here,$(a, a), (b, b), (c, c) \in R$,so $R$ is reflexive.$2$. Symmetry: For a relation to be symmetric,if $(x, y) \in R$,then $(y, x) \in R$. Here,$(a, c) \in R$ but $(c, a) 
otin R$. Therefore,$R$ is not symmetric.$3$. Transitivity: For a relation to be transitive,if $(x, y) \in R$ and $(y, z) \in R$,then $(x, z) \in R$. The pairs are $(a, a), (b, b), (c, c), (a, c)$. Checking $(a, c) \in R$ and $(c, c) \in R$,we get $(a, c) \in R$. All conditions for transitivity are satisfied. Thus,$R$ is transitive.Conclusion: The relation is reflexive and transitive but not symmetric. The correct option is $B$.

$A$ relation $R$ defined on the set $A = \{a, b, c\}$ is given by $R = \{(a, a), (b, b), (c, c), (a, c)\}$. This relation is . . . . . . .

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