The relation "less than" in the set | vedclass

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

Question

(B) Let $R$ be the relation "less than" $( < )$ defined on the set of natural numbers $N$.
$1$. Reflexivity: For a relation to be reflex

Vedclass · Accepted Answer

Only transitive

Vedclass · Answer

(B) Let $R$ be the relation "less than" $( < )$ defined on the set of natural numbers $N$.
$1$. Reflexivity: For a relation to be reflexive,$xRx$ must hold for all $x \in N$. Since $x < x$ is false for any natural number $x$,the relation is not reflexive.
$2$. Symmetry: For a relation to be symmetric,$xRy$ must imply $yRx$. If $x < y$,it does not imply $y < x$ (e.g.,$1 < 2$ but $2 
ot < 1$). Thus,the relation is not symmetric.
$3$. Transitivity: For a relation to be transitive,$xRy$ and $yRz$ must imply $xRz$. If $x < y$ and $y < z$,then it is always true that $x < z$. Therefore,the relation is transitive.
Conclusion: The relation "less than" is only transitive.

The relation "less than" in the set of natural numbers is

Similar Questions

Let $R$ be a relation from $Q$ to $Q$ defined by $R = \{(a, b) : a, b \in Q \text{ and } a - b \in Z \}$. Show that $(a, b) \in R$ and $(b, c) \in R$ implies that $(a, c) \in R$.

Let $L$ be the set of all straight lines in a plane and the relation $R$ on $L$ is defined by $\alpha R \beta \Leftrightarrow \alpha \perp \beta$,where $\alpha, \beta \in L$. Then $R$ is:

Let $R$ be a relation on the set $A$ of ordered pairs of positive integers defined by $(x, y) R (u, v)$ if and only if $xv = yu$. Show that $R$ is an equivalence relation.

How many reflexive relations are there on a set with $3$ elements?

Define a relation $R$ on the interval $[0, \frac{\pi}{2})$ by $xRy$ if and only if $\sec^2 x - \tan^2 y = 1$. Then $R$ is :

Vedclass Test Series

Exam Paper Generator

Online Exam Module