Login/Sign Up
Home » A relation R is defined from a set A = {2, 3, 4, 5} to a set B = {3, 6, 7, 10} as follows: (x, y) R x is relatively prime to y. Express R as a set of ordered pairs and determine its domain and range.
A relation R is defined from a set A = {2, 3, 4, 5} to a set B = {3, 6, 7, 10} as follows: (x, y) R x is relatively prime to y. Express R as a set of ordered pairs and determine its domain and range.
CBSE | Class 11 | Exercise 2.3 | Maths | RD Sharma | Relations
A relation R is defined from a set A = {2, 3, 4, 5} to a set B = {3, 6, 7, 10} as follows: (x, y) R x is relatively prime to y. Express R as a set of ordered pairs and determine its domain and range.

Solution:

Co-prime numbers are numbers that are close to being prime if there isn’t a greater than one integer that divides both (that is, their greatest common divisor is one).

It is given that: (x, y) ∈ R = x is relatively prime to y

In this case, we can see that:

2 is a co-prime number to 3 and 7.

3 is a co-prime number to 7 and 10.

4 is a co-prime number to 3 and 7.

5 is a co-prime number to 3, 6 and 7.

Therefore, we can write

R=\left\{ \left( 2,\text{ }3 \right),\text{ }\left( 2,\text{ }7 \right),\text{ }\left( 3,\text{ }7 \right),\text{ }\left( 3,\text{ }10 \right),\text{ }\left( 4,\text{ }3 \right),\text{ }\left( 4,\text{ }7 \right),\text{ }\left( 5,\text{ }3 \right),\text{ }\left( 5,\text{ }6 \right),\text{ }\left( 5,\text{ }7 \right) \right\}

The domain of the relation is given by:

\text{Domain}=\left\{ 2,\text{ }3,\text{ }4,\text{ }5 \right\}

and the range of the relation is:

Range=\left\{ 3,\text{ }6,\text{ }7,\text{ }10 \right\}

i

More Material