Download App

RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS1 Mark
Question
Choose the correct answer from the given four options.
Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then R is:
  1. Symmetric but not transitive.
  2. Transitive but not symmetric.
  3. Neither symmetric nor transitive.
  4. Both symmetric and transitive.
✓

Answer

  1. Transitive but not symmetric.

Solution:

We are given that a relation R defined aRb ⇒ a is brother of b.

aRa ⇒ a is brother of a, which is not true.

Hence, R is not reflexive.

aRb ⇒ a is brother of b.

This does not mean b is also a brother of a and b can be a sister of a.

Hence, it is not symmetric.

aRb ⇒ a is brother of b

and bRc ⇒ b is a brother of c.

So, a is brother of c.

Hence, R is 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 "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 set of equations $x - y + 3z = 2 , 2x - y + z = 4 , x - 2y + \alpha z = 3$ has
→
The value of $\int\limits^\frac{\pi}{2}_0\log\Big(\frac{4+3\sin\text{x}}{4+3\cos\text{x}}\Big)\text{dx}$ is:
  1. 2
  2. $\frac{3}{4}$
  3. 0
  4. -2
→
Let $p$ and $q$ be the position vectors of $P$ and $Q$ respectively with respect to $O$ and $|p|\, = p,\,\,|q|\,\, = q.$ The points $R$ and $S$ divide $PQ$ internally and externally in the ratio $2 : 3$ respectively. If $\overrightarrow {OR} $ and $\overrightarrow {OS} $ are perpendicular, then
→
If ${A_\lambda } = \left( {\begin{array}{*{20}{c}}
\lambda &{\lambda  - 1}\\
{\lambda  - 1}&\lambda 
\end{array}} \right);\,\lambda  \in N$ then $|A_1| + |A_2| + ..... + |A_{300}|$ is equal to
→
If the vectors $2i - j + k,\,\,i + 2j - 3k$ and $3i + \lambda j + 5k$ be coplanar, then $\lambda = $
→
Let $R$ be a relation on $Z \times Z$ defined by$ (a, b)$$R(c, d)$ if and only if $ad - bc$ is divisible by $5$ . Then $\mathrm{R}$ is
→
Area of curve explained in the passage from $0 \text{ to}\frac{\pi}{2}\text{ is:}$
  1. $\frac{1}{3}\text{ sq.}\text{ unit}$
  2. $\frac{1}{2}\text{ sq.}\text{ unit}$
  3. $1\text{ sq.}\text{ unit}$
  4. $2\text{ sq.}\text{ units}$
→
The function f(x) = x2e-x is monotonic increasing when:

  1. $\text{x}\in\text{R}-[0,2]$

  2. $0<\text{x}<2$

  3. $2<\text{x}<\infty$

  4. $\text{x}<0$

→
The maximum value of  $xy $ when $x + 2y = 8$ is
→
If A and B are two events such that $\text{P(A)}=\frac{1}{2},\text{P(B)}=\frac{1}{3},\text{P}(\text{A}|\text{B})=\frac{1}{4},$ then $\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$ equals.
  1. $\frac{1}{12}$
  2. $\frac{3}{4}$
  3. $\frac{1}{4}$
  4. $\frac{3}{16}$
→