Give an example of a relation which is, Reflexive and symmetric b… - Vidyadip

Question

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

✓

Answer

Let A = {4, 6, 8}

Define a relation R on A as:

A = {(4, 4), (6, 6), (8, 8), (4, 6), (6, 4), (6, 8), (8, 6)}

Relation R is reflexive since for every $\text{a}\in\text{A},\ (\text{a, a})\in\text{R}$ i.e., (4, 4), (6, 6), (8, 8) $\in\text{R}$

Relation R is symmetric since $(\text{a, b})\in\text{R}\Rightarrow\ (\text{b, a})\in\text{R}$ for all $\text{a, b}\in\text{R.}$

Relation R is not transitive since (4, 6), (6, 8) $\in\text{R,}$ but $(4,8)\notin\text{R.}$

Hence, relation R is reflexive and symmetric but not transitive.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks" from Relations→Relations — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Write a value of $\int\frac{1+\log\text{x}}{3+\text{x}\log\text{x}}\text{ dx}$

If the line has direction ratios 2, -1, -2 determine its direction Cosines.

Show that the function given by f(x) = $\frac{\log x}{x}$ has maximum at x = e.

An urn contains 3 white, 4 red and 5 black balls. Two balls are drawn one by one without replacement. What is the probability that at least one ball is black?

Differentiate the following functions with respect to x:
$3^{\text{x}\log\text{x}}$

Find the value of $\lambda$ so that the following vectors are coplanar:
$\vec{\text{a}}=\hat{\text{i}}+2\hat{\text{j}}-3\hat{\text{k}},\vec{\text{b}}=3\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}},\vec{\text{c}}=\hat{\text{i}}+2\hat{\text{j}}+2\hat{\text{k}}$

Verify that $\text{y}=4\sin3\text{x}$ is a solution of the differential equation $\frac{\text{d}^2\text{y}}{\text{dx}^2}+9\text{y}=0.$

If $\text{A}=\begin{bmatrix}\cos\alpha&\sin\alpha\\-\sin\alpha&\cos\alpha\end{bmatrix},$ and $\text{A}^{-1}=\text{A}',$ find value of $\alpha.$

Evaluate the following integrals:
$\int\frac{(\text{x}+1)\text{e}^\text{x}}{\cos^2(\text{xe}^\text{x})}\text{ dx}$

Differentiate the following w.r.t. x:
$(\sin\text{x})^{\cos\text{x}}$