On set A = {1, 2, 3}, relations R and S are g | vedclass

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(C) Given $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)\}$ and $S = \{(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)\}$.$R \cup S = \{(1, 1), (2, 2), (3, 3),

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$R \cup S$ is reflexive and symmetric but not transitive

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(C) Given $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)\}$ and $S = \{(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)\}$.$R \cup S = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (1, 3), (3, 1)\}$.$1$. Reflexivity: Since $(1, 1), (2, 2), (3, 3) \in R \cup S$, it is reflexive.$2$. Symmetry: Since $(1, 2) \in R \cup S \implies (2, 1) \in R \cup S$ and $(1, 3) \in R \cup S \implies (3, 1) \in R \cup S$, it is symmetric.$3$. Transitivity: We have $(2, 1) \in R \cup S$ and $(1, 3) \in R \cup S$. If it were transitive, $(2, 3)$ must be in $R \cup S$. However, $(2, 3) 
otin R \cup S$. Thus, it is not transitive.Therefore, $R \cup S$ is reflexive and symmetric but not transitive.

On set $A = \{1, 2, 3\}$, relations $R$ and $S$ are given by $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)\}$ and $S = \{(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)\}$. Then,

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