Maths-

General

Easy

Question

# If the relation R: A → B, where A = {2, 3, 4} and B = {3, 5} is defined by R = {(x, y):x < y, x ϵ A, y ϵ B}, then find R^{-1}

Hint:

### The inverse function returns the original value for which a function gave the output. If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x. A function that consists of its inverse fetches the original value. Example: f(x) = 2x + 5 = y. Then, g(y) = (y-5)/2 = x is the inverse of f(x).

## The correct answer is: {(x, y):x >= y, x ϵ A, y ϵ B}

### We have given the Relation R: A → B

A = {2, 3, 4}

B = {3, 5}

We have given the relation in Set- builder form ,

R = {(x, y):x < y, x ϵ A, y ϵ B}

We will first find the Cartesian product of set A and B

A X B = {(2,3),(2,5),(3,3),(3,5)(4,3),(4,5)}

R = {(2,3),(2,5),(3,5),(4,5)}

Therefore, R^{-1} = (A X B) – R

R^{-1} = {(3,3),(4,3)}

R^{-1} = {(x, y):x >= y, x ϵ A, y ϵ B}

We have given the relation in Set- builder form ,

We will first find the Cartesian product of set A and B

^{-1}= (A X B) – R

^{-1}= {(3,3),(4,3)}

^{-1}= {(x, y):x >= y, x ϵ A, y ϵ B}