Download App

Relations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations3 Marks
Question
Three relation R2 is defined in set A = {a, b, c} as follows:
R2 = {(a, a)}
Find whether or not the relation R2 on A is:
  1. Reflexive.
  2. Symmetric.
  3. Transitive.
✓

Answer

R2 is Reflexive: Clearly $\text{a, a}\in\text{R}_2$
Therefore, R2 is reflexive.
Symmetric: Clearly, $\text{a, a}\in\text{R}\Rightarrow\ \text{a, a}\in\text{R}.$
Therefore, R2 is symmetric.
Transitive: R2 is clearly a transitive relation, since there is only one element in it.

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 the plane $\vec{\text{r}}.(2\hat{\text{i}}+3\hat{\text{j}}-6\hat{\text{k}})=14$ in normal form.
→
Evaluate the following integrals:
$\int^\limits{9}_4\frac{\sqrt{\text{x}}}{\big(30-\text{x}^{\frac{3}{2}}\big)^2}\text{ dx}$
→
Evaluate the following integrals:
$\int^\limits{\frac{\pi}{4}}_{\frac{-\pi}{4}}|\sin\text{x}|\text{dx}$
→
Determine the binomial distribution for which the mean is 20 and variance 16.
→
Differentiate the following functions with respect to x:
$\tan5\text{x}^\circ$
→
If x < 1, then write the value of $\cos^{-1}\Big(\frac{1-\text{x}^2}{1+\text{x}^2}\Big)$ in terms of $\tan^{-1}\text{x.}$
→
By using the properties of definite integral, evaluate the integral in Exercise:
$\int\limits_{2}^{8}|\text{x}-5|\ \text{dx}$
→
Evalute the following integrals:
$\int\frac{1}{\sqrt{1-\text{x}^2}(2+3\sin^{-1}\text{x})}\text{dx}$
→
If $\text{A}=\begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}\text{ and A (adj A =)}\begin{bmatrix} \text{k} & 0 \\ 0 & \text{k} \end{bmatrix},$ then find the value of k.
→
Find which of the function:
$\text{f(x)}=\begin{cases}\frac{|\text{x}-4|}{2(\text{x}-4)},&\text{if x}\neq4\\0,&\text{if x}=4\end{cases}$
at x = 4
→