Question

If A = {2, 3, 4}, B = {1, 3, 7} and R = {(x, y) : x ∈ A, y ∈ B and x ≤ y} is a relation from A to B,

then domain of R is………………​

Answer 1

Answer:

Domain of R = {2,3,4}

Step-by-step explanation:

Given :-

A = {2, 3, 4},

B = {1, 3, 7}

and R = {(x, y) : x ∈ A, y ∈ B and x ≤ y} is a relation from A to B,

To find :-

Find the domain of R ?

Solution :-

Given sets are :

A = {2, 3, 4}

=> n(A) = 3

B = {1, 3, 7}

=> n(B) = 3

We know that

If number of elements in A is m and the number of elements in B is n then total number of relations from A to B is 2^mn

Total number of relations from A to B

= 2^(3×3)

= 2⁹

Given relation from A to B = R

R is defined as R = {(x, y) : x ∈ A, y ∈ B and x ≤ y}

=> R = { (2,3),(2,7),(3,1),(3,3),(3,7),(4,1),(4,3),(4,7)}

The set of all first elements of order pairs = {2,3,4}

Domain of R = {2,3,4}

Answer:-

Domain of R for the given problem is {2,3,4}

Used formulae:-

• If number of elements in A is m and the number of elements in B is n then total number of relations from A to B is 2^mn

• The set of all first elements of ordered pairs (x-coordinates) is called its Domain.