Download App

Relations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations2 Marks
Question
Is it true that every relation which is symmetric and transitive is also reflexive? Give reasons.
✓

Answer

No, it is not necessary that a relation which is symmetric and transitive is reflexive as well.
For Example,
Let A = {a, b, c} be a set and
R2 = {(a, a)} is a relation defined on A.
Clearly,
R2 is symmetric and transitive but not reflexive.

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" 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

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are the position vectors of the vertices of a triangle, then write the position vector of its centroid.
→
Examine whether the operation * defined on R by $\text{a}^*\text{b}=\text{ab}+1$ is (i) a binary or not. (ii) if a binary operation, is it associative or not?
→
Find the vector equation of the line passing through the point A(1, 2, –1) and parallel to the line $\text{5x – 25 = 14 – 7y = 35z.}$
→
For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.
$\text{y}=\text{a e}^{\text{x}}+\text{b e}^{-\text{x}}+\text{x}^2$ : $\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}+2\frac{\text{dy}}{\text{dx}}-\text{xy}+\text{x}^2-2=0$
→
Differentiate the following w.r.t.x: $\cos({\log\text{x}}+\text{e}^{\text{x}}),\text{x}>0$
→
For given vectors, $\vec{a}=2\hat{i}-\hat{j}+2\hat{k}\ \ \text{and}\ \vec{b}=-\hat{i}+\hat{j}-\hat{k},$ find the unit vector in the direction of the vector $\vec{a}+\vec{b}.$
→
If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p.
→
Evaluate the following integrals:
$\int\Big(\frac{\text{m}}{\text{x}}+\frac{\text{x}}{\text{m}}+\text{m}^\text{x}+\text{x}^\text{m}+\text{mx}\Big)\text{dx}$
→
An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.
→
Differentiate the function with respect to x : $\sec \left( {\tan \sqrt x } \right)$
→