Give an example of a relation which is,Symmetric but neither refl… - Vidyadip

Question

Give an example of a relation which is,Symmetric but neither reflexive nor transitive.

✓

Answer

Let A = {5, 6, 7}.
Define a relation R on A as R = {(5, 6), (6, 5)}.
Relation R is not reflexive as $(5, 5), (6, 6), (7, 7)\notin\text{R.}$ $$
Now, as $(5, 6)\in\text{R}$ and also $(6,5)\in\text{R,}$ R is symmetric.
$\Rightarrow(5, 6), (6, 5)\in\text{R,}\text{but}(5, 5)\notin\text{R}$ $$ $$ $$
Therefore, R is not transitive.
Hence, relation R is symmetric but not reflexive or 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 Question" 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

Find the coordinates of the foot of the perpendicular and its length drawn from the point $P(5,4,2)$ to the line
$
\vec{r}=-\hat{i}+3 \hat{j}+\hat{k}+\lambda \quad(2 \hat{i}+3 \hat{j}-\hat{k})
$

A fair die is tossed twice. If the number appearing on the top is less than 3, it is success. Find the probability distribution of number of successes.

ABCDE is a pentagon, prove that,$\overrightarrow{\text{AB}}+\overrightarrow{\text{BC}}+\overrightarrow{\text{CD}}+\overrightarrow{\text{DE}}+\overrightarrow{\text{EA}}=\vec0$

Test whether the following relations $R_2$ are:

Reflexive.
Symmetric.
Transitive.

$R_2$ on Z defined by $(\text{a, b})\in\text{R}_2\Leftrightarrow\ |\text{a}-\text{b}|\leq5$

If a, b, c are non-zero real numbers and if the system of equations

(a - 1)x = y + z

(b - 1)y = z + x

(c - 1)z = x + y

has a non-trivial solution, then prove that ab + bc + ca = abc.

Find the vector equations of the following planes in scalar product form $(\vec{\text{r}}\cdot\vec{\text{n}}=\text{d}):$
$\vec{\text{r}}=\hat{\text{i}}-\hat{\text{j}}+\lambda(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}})+\mu(4\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}})$

Evaluate the following:
$\tan^{-1}\Big(\tan\frac{5\pi}{6}\Big)+\cos^{-1}\Big\{\cos\Big(\frac{13\pi}{6}\Big)\Big\}$

If $x = a \left(\cos t+\log \tan \frac{t}{2}\right), y = a \sin t$, then evaluate $\frac{d^2 y}{d x^2}$ at $t=\frac{\pi}{3}$.

Classify the following functions as injection, surjection or bijection:
$f : Z \rightarrow Z$ given by $f(x) = x^2$

Write the following in the simplest form:
$\tan^{-1}\Big\{\text{x}+\sqrt{1+\text{x}^2}\Big\},\text{x}\in\text{R}$