Download App

RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS1 Mark
Question
Let R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. Then, R is:
  1. Identify relation.
  2. Reflexive.
  3. Symmetric.
  4. Antisymmetric.
✓

Answer

  1. Reflexive.

Solution:

Reflexivity: Since $(\text{a, a})\in\text{R}\ \forall\ \text{a}\in\text{A},$ R is reflexive on A.

Symmetry: Since $(\text{a, b})\in\text{R}$ but $(\text{b, a})\notin\text{R,}$ is not symmetric on A.

⇒ R is not antisymmetric on A.

Also, R is not an identity relation on A.

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 "M.C.Q (1 Marks)" 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

The order of the differential equation of all circles of radius $r$, having centre on $y$-axis and passing through the origin is
→
If the matrices has 13 elements , then the possible dimension (order) it can have are:
  1. 1 × 13 or 13 × 1
  2. 1 × 26 or 26 × 1
  3. 2 × 13 or 13 × 2
  4. None of these
→
If $\text{P(A)}=\frac{3}{10},\text{P(B)}=\frac{2}{5}$ and $\text{P}(\text{A}\cap\text{B}=\frac{3}{5,}$ then P(A|B) + P(B|A) equals
  1. $\frac{1}{4}$
  2. $\frac{7}{12}$
  3. $\frac{5}{12}$
  4. $\frac{1}{3}$
→
The area bounded between the parabola $y^2 = 4x$ and the line $2x + y -4 = 0$ is
→
If $\int {\frac{{\cos e{c^2}x}}{{{{\left( {\cos ec\,x\, + \,\cot \,x} \right)}^{\frac{9}{2}}}}}\,dx} $ = ${\left( {\cos ec\,x\, - \,\cot \,x} \right)^{\frac{7}{2}}}\left( {\frac{1}{\alpha } + \frac{{{{\left( {\cos ec\,x\, - \,\cot \,x} \right)}^2}}}{{11}}} \right) + \,C$ (where $C$ is constant of integration and $\alpha \in N)$ , then $\alpha $ is 
→
The area of the region enclosed by the parabola $(y-2)^2=x-1$, the line $x-2 y+4=0$ and the positive coordinate axes is
→
The minimum number of times one has to toss a fair coin so that the probability; of observing at least one head is at least $90\%$ is
→
The number of possible matrices of order 3×3 with each entry 2 or 0 is:
  1. 9
  2. 27
  3. 81
  4. None of these.
→
A bag contains $N$ balls out of which $3$ balls are white, $6$ balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For $i=1,2,3$, let $W_l, G_l$, and $B_l$ denote the events that the ball drawn in the $i^{\text {mh }}$ draw is a white ball, green ball, and blue ball, respectively, If the probability $P\left(W_1 \cap G_2 \cap B_3\right)=\frac{2}{5 N}$ and the conditional probability $P\left(B_3 \mid W_1 \cap G_2\right)=\frac{2}{9}$, then $N$ equals. . . .
→
Let $R$ be a relation over the set $N × N$ and it is defined by $(a,\,b)R(c,\,d) \Rightarrow a + d = b + c.$ Then $R$ is
→