Let A = a, b . List all relations on A and find their number. - Vidyadip

Question

Let A = {a, b}. List all relations on A and find their number.

✓

Answer

Here, A = {a, b} We know that, Number of relations $= 2^{m\times n} = 2^{2\times 2} = 24 = 16$ Number of relations on A = 16 Relations on A are given by, R = {a, a}, {a, b}, {b, a}, {b, b}, {(a, a), (a, b)}, {(a, a), (b, a)}, {(a, a), (b, b)}, {(a, b), (b, a)}, {(a, b), (b, b)} {(b, a), (b, b)}, {(a, a), (a, b), (b, a)}, {(a, b), (b, a), (b, b)}, {(b, a), (b, b), (a, a)}, {(b, b), (a, a), (a, b)}, {(a, a), (b, a), (b, b)}, {(a, a), (b, a), (b, b)}

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 "(Each question 3 marks)" from Relation→Relation — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.

If $\sin\text{x}=\frac{\text{a}^2-\text{b}^2}{\text{a}^2+\text{b}^2}$ find the value of $\tan\text{x},\sec\text{x}$ and $\text{cosec x}$

Show the following quadratic equation by factorization method: $\text{x}^2+\frac{\text{x}}{\sqrt{2}}+1=0$

Solve the following system of equations in R. $|3-4\text{x}|\geq9$

Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.

Let A = {x : x $\in$ N}, B = {x : x = 2n, n $\in$ N}, C = {x : x = 2n - 1, n $\in$ N} and D = {x : x is a prime natural number}. Find: $\text{B}\cap\text{C}$

Show that the three points A(2, 3, 4), B(-1, 2, -3) and C(-4, 1, -10) are collinear and find the ratio in which C divides AB.

It is required, to seat 5 men, and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

Solve the following system of equations in R. $\Big|\text{x}+\frac{1}{3}\Big|>\frac{8}{3}$

Let A = {x : x $\in$ N}, B = {x : x = 2n, n $\in$ N}, C = {x : x = 2n - 1, n $\in$ N} and D = {x : x is a prime natural number}. Find:
$\text{A}\cap\text{B}$