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 = {3,4,5}
Define a relation R on A as R = {(3,4), (4,3)}
Relation R is not reflexive as (3,3), (4,4) ,(5,5) $\notin$ R.
Now, as (3,4) $\in$ R and (4,3) $\in$ R,
R is symmetric.
Further, (3,4),(4,3) $\in$ R, but (3,3) $\notin$ R
$\Rightarrow$ R is not transitive.
Therefore, 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 "2 Marks Questions" from Relations and Functions→Relations and Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\begin{bmatrix}2&1&3 \end{bmatrix}$ $\begin{pmatrix}-1&0&-1\\-1&1&0\\0&1&1 \end{pmatrix}\begin{pmatrix}1\\0\\-1 \end{pmatrix}=\text{A},$ then write the order of matrix A.

An unbiased die with face marked 1, 2, 3, 4, 5, 6 is rolled four times. Out of 4 face values obtained, find the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5.

Evaluate $\int_0^\pi \frac{e^{\cos x}}{e^{\cos x}+e^{-\cos x}} d x$.

A stone is dropped into a quiet lake and waves move in circles at a speed of 4cm/ sec. At the instant when the radius of the circular wave is 10cm, how fast is the enclosed area increasing?

If matrix $A = [1 2 3]$, write $AA^T$.

Evaluate the following integrals:
$\int\limits^\frac{\pi}{2}_0\cos^2\text{x}\text{ dx}$

Prove that the function $\text{f}(\text{x})=\cos\text{x}$ is:
Neither increasing nor decreasing in $(0,2\pi)$

Write a value of $\int\frac{\sec^2\text{x}}{(5+\tan\text{x})^4}\text{ dx}$

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two vectors such that $\big(\vec{\text{a}}+\vec{\text{b}}\big).\big(\vec{\text{a}}-\vec{\text{b}}\big).=0,$ find the relation betwen the magnitudes of $\vec{\text{a}}$ and $\vec{\text{b}}.$

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are three mutually perpendicular unit vectors, then prove that $\big|\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big|=\sqrt{3}$