Choose the correct answer from the given four options. Consider t… - Vidyadip

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:

Symmetric but not transitive.
Transitive but not symmetric.
Neither symmetric nor transitive.
Both symmetric and transitive.

✓

Answer

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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Let $\begin{vmatrix}\text{x}&2&\text{x}\\\text{x}^2&\text{x}&6\\\text{x}&\text{x}&6\end{vmatrix}=\text{ax}^4+\text{bx}^3+\text{cx}^2+\text{dx}+\text{e}.$ Then, the value of $5a + 4b + 3c + 2d + e$ is equal to:

If the binary operation $*$ on $Z$ is defined by $a * b = a^2 − b^2 + ab + 4,$ then value of $(2 * 3) * 4$ is:

If $A$ is a symmetric matrix and $n \in N$, then $A^n$ is a

Choose the correct answer from the given four options.
The probability distribution of a discrete random variable X is given below:

$\text{X}$	$2$	$3$	$4$	$5$
$\text{P}(\text{X})$	$\frac{5}{\text{k}}$	$\frac{7}{\text{k}}$	$\frac{9}{\text{k}}$	$\frac{11}{\text{k}}$

The value of k is:

8.
16.
32.
48.

The set of all points where the function $f(x)=x+|x|$ is differentiable, is

Using determinants, find the area $($in sq. units$)$ of triangle with vertices $(-3,5),(3,-6)$ and $(7,2)$.

The value of $\int_0^{\pi / 6} \sin 3 x\ d x$ is:

For the function $\text{f}(\text{x})=\text{x}+1\text{x},\text{x}\in[1,3],$ the value of c for the Lagrange's mean value theorem is:

1
$\sqrt3$
2
none of these

The probablity of selecting a male or a female is same. If the probability that in an office of n persons (n - 1) males being selected is $\frac{3}{2^{10}},$ the value of n is:

The function $f : R \rightarrow R$ defined by $f(x) = 2^x + 2^{|x|}$ is: