Let R be a relation on the set of real number | vedclass

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(B) relation $R$ on the set of real numbers $\mathbb{R}$ is defined by $nm \ge 0$.$1$. Reflexive: For any $n \in \mathbb{R}$,$n \cdot n = n^2 \ge 0$.

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Reflexive and symmetric

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(B) relation $R$ on the set of real numbers $\mathbb{R}$ is defined by $nm \ge 0$.$1$. Reflexive: For any $n \in \mathbb{R}$,$n \cdot n = n^2 \ge 0$. Thus,$(n, n) \in R$. So,$R$ is reflexive.$2$. Symmetric: If $(n, m) \in R$,then $nm \ge 0$. Since $nm = mn$,it follows that $mn \ge 0$,so $(m, n) \in R$. Thus,$R$ is symmetric.$3$. Transitive: Consider $(n, m) \in R$ and $(m, p) \in R$. This means $nm \ge 0$ and $mp \ge 0$. If $n=1, m=0, p=-1$,then $1 \cdot 0 = 0 \ge 0$ and $0 \cdot (-1) = 0 \ge 0$,but $n \cdot p = 1 \cdot (-1) = -1 Therefore,$R$ is reflexive and symmetric.

Let $R$ be a relation on the set of real numbers defined by $nm \ge 0$. Then $R$ is:

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