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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

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

Vedclass · Accepted Answer

Reflexive and symmetric

Vedclass · Answer

(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:

Similar Questions

Let $A = \{2, 3, 4\}$ and $B = \{8, 9, 12\}$. Then the number of elements in the relation $R = \{((a_1, b_1), (a_2, b_2)) \in (A \times B) \times (A \times B) : a_1 \text{ divides } b_2 \text{ and } a_2 \text{ divides } b_1\}$ is:

The relation $R$ defined in the set of natural numbers $N$ as $aRb \iff b$ is divisible by $a$ is:

If $n(A) = m$,then the total number of reflexive relations that can be defined on $A$ is-

Let $A = \{2, 3, 4, 5, \ldots, 30\}$ and $\simeq$ be an equivalence relation on $A \times A$,defined by $(a, b) \simeq (c, d)$ if and only if $ad = bc$. Then the number of ordered pairs $(c, d)$ which satisfy this equivalence relation with the ordered pair $(4, 3)$ is equal to:

Give an example of a relation which is reflexive and transitive but not symmetric.

Vedclass Test Series

Exam Paper Generator

Online Exam Module