Source: Extra Practice
Consider the relation R = {(x, y) : x, y ∈ Z, x^2 + y^2 = 9}. Which of the following is NOT an element of the domain of R?
Options
Option A
0
Option B
3
Option C
-3
Option D is correct
2
Explanation
For x to be in the domain, there must exist an integer y such that x^2 + y^2 = 9. If x=0, y²=9 (y=±3). If x=3, y²=0 (y=0). If x=-3, y²=0 (y=0). If x=2, y² = 9 - 4 = 5. Since √5 is not an integer, x=2 cannot be in the domain of a relation defined over integers Z. Thus, 2 is the correct answer. All other options result in integer values for y.