Question

Determine the domain and range of the following relations:

(i) R1 ={x∣x=1,0(ii) R2 ={3x,x∣x is a prime number less than 10 )

Answer 1

The domain of R1 is {1, 0}, and its range is also {1, 0}. The domain of R2 is {2, 3, 5, 7}, and the range is {6, 9, 15, 21}.

Step-by-step explanation:

To determine the domain and range of the given relations we need to analyze each one carefully:

1. For the first relation, R1 = {x‒x=1,0), the domain is simply the values that x can take, which in this case are explicitly given as 1 and 0. Therefore, the domain of R1 is {1, 0}. The range is also {1, 0} because these are the values that x equals to in this relation.

2. For the second relation, R2 = {3x, x‒x is a prime number less than 10), we must identify all prime numbers less than 10. These are 2, 3, 5, and 7. The domain of R2 is thus {2, 3, 5, 7}. Since we are taking each of these primes x and multiplying them by 3, the range for the relation will be the set {6, 9, 15, 21}.