Maths-

General

Easy

Question

# A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.

Hint:

### Cartesian product of A and B is denoted by A X B and it is defined as set og all ordered pairs (a, b) such that

## The correct answer is: {(1,4),(1,6),(2,9),(3,4),(3,6),(5,4),(5,6)}

### We have given the two sets

A = {1, 2, 3, 5} and B = {4, 6, 9}

And

R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}

First of all we will find the cartesian product of set A and set B

A X B = {(1,4),(1,6),(1,9),(2,4),(2,6),(2,9),(3,4),(3,6),(3,9),(5,4),(5,6),(5,9)}

We have relation R , with condition difference between x and y is odd, in this cartesian product we will find out the points satisfying the condition.

So, R in roaster form is

R = {(1,4),(1,6),(2,9),(3,4),(3,6),(5,4),(5,6)}

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### Which of the following relations are functions? Give reasons.

(i) {(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)}

(ii) {(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)}

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(ii) {(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)}

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