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(A) First,check for symmetry:For $R_1$: $(c, a) \in R_1$ but $(a, c) \in R_1$. However,$(b, c) \in R_1$ but $(c, b) 
otin R_1$. Thus,$R_1$ is not sym

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$R_2$ is symmetric but it is not transitive

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(A) First,check for symmetry:For $R_1$: $(c, a) \in R_1$ but $(a, c) \in R_1$. However,$(b, c) \in R_1$ but $(c, b) 
otin R_1$. Thus,$R_1$ is not symmetric.For $R_2$: $(a, b) \in R_2$ and $(b, a) \in R_2$. $(a, c) \in R_2$ but $(c, a) \in R_2$. $(c, a) \in R_2$ but $(a, c) \in R_2$. Thus,$R_2$ is symmetric.Next,check for transitivity:For $R_1$: $(b, c) \in R_1$ and $(c, a) \in R_1$,but $(b, a) 
otin R_1$. Thus,$R_1$ is not transitive.For $R_2$: $(b, a) \in R_2$ and $(a, c) \in R_2$,but $(b, c) 
otin R_2$. Thus,$R_2$ is not transitive.Conclusion: $R_2$ is symmetric but not transitive,and $R_1$ is neither symmetric nor transitive.

Consider the following two binary relations on the set $A = \{a, b, c\}$: $R_1 = \{(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)\}$ and $R_2 = \{(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)\}$. Then

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