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On the set A = {1, 2, 3, 4, 5}, consider the relation R defined by R = {(x, y): |x² - y²| < 16}. Which of the following sets represents R?

1. {(1,1), (2,1), (3,1), (4,1), (2,3)}
2. {(2,2), (3,2), (4,2), (2,4)}
3. {(3,3), (3,4), (5,4), (4,3), (3,1)}
4. None of these

Correct answer: None of these

Solution

R = {(x,y): |x^2-y^2|<16} on {1..5} contains 19 ordered pairs (e.g. (1,1),(1,2),(1,3),(1,4),(2,1)...,(4,5),(5,4),(5,5)). None of the small listed sets equals R, so the answer is 'None of these'.

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