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In Mathematics / High School | 2025-07-03

If a relation R = {(a, a²) : a ∈ A and a² ∈ A} is defined on A × A and the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9}, what will be the range of R?

(A) {1, 4}
(B) {1, 2, 3}
(C) {1, 4, 9}
(D) None of these

Asked by Vvswift7613

Answer (1)

To determine the range of the relation R = {( a , a 2 ) : a ∈ A and a 2 ∈ A } where the set A = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } , let's follow these steps:

Identify the Domain : The domain A includes the numbers {1, 2, 3, 4, 5, 6, 7, 8, 9}.

Calculate Each Square : Find the square of each number in A .



1 2 = 1

2 2 = 4

3 2 = 9

4 2 = 16

5 2 = 25

6 2 = 36

7 2 = 49

8 2 = 64

9 2 = 81



Determine Which Squares Are in A : We only consider the squares that are also in the set A .


Only 1 2 = 1 , 2 2 = 4 , and 3 2 = 9 are in set A .


List the Range : Therefore, the range of R is {1, 4, 9}.

Based on the calculations, the correct option is (C) {1, 4, 9} .

Answered by SophiaElizab | 2025-07-06

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