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(N/A) Given the relation $R = \{(a, b) : a \leq b\}$ on the set of real numbers $\mathbb{R}$.$1$. Reflexive: For any $a \in \mathbb{R}$,we know that $

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(N/A) Given the relation $R = \{(a, b) : a \leq b\}$ on the set of real numbers $\mathbb{R}$.$1$. Reflexive: For any $a \in \mathbb{R}$,we know that $a \leq a$ is always true. Therefore,$(a, a) \in R$ for all $a \in \mathbb{R}$. Hence,$R$ is reflexive.$2$. Symmetric: Consider $(2, 4) \in R$ because $2 \leq 4$. However,$(4, 2) 
otin R$ because $4 
ot\leq 2$. Since $(a, b) \in R$ does not imply $(b, a) \in R$,the relation is not symmetric.$3$. Transitive: Let $(a, b) \in R$ and $(b, c) \in R$. This means $a \leq b$ and $b \leq c$. By the transitive property of inequality,$a \leq c$. Therefore,$(a, c) \in R$. Hence,$R$ is transitive.Conclusion: The relation $R$ is reflexive and transitive but not symmetric.

Show that the relation $R$ in the set of real numbers $\mathbb{R}$ defined as $R = \{(a, b) : a \leq b\}$ is reflexive and transitive but not symmetric.

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