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A relation R is defined on the set of integers Z by the condition that (x,y) belongs to R exactly when x² + y² = 9. Which statement below is false?

1. R = {(0,3), (0,-3), (3,0), (-3,0)}
2. The domain of R is {-3, 0, 3}
3. The range of R is {-3, 0, 3}
4. None of these

Correct answer: None of these

Solution

Integer solutions of x^2+y^2=9 are (0,+/-3) and (+/-3,0). The relation set, its domain {-3,0,3}, and its range {-3,0,3} are all stated correctly. Since none of statements (a)-(c) is false, the false-statement answer is 'None of these'.

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