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Let A = {1, 2, 3,..., 10} be the set of the first ten natural numbers, and let R be the relation on A defined by R = { (x, y): x ∈ A, y ∈ A and x + 2y = 10 }. What is the range of R?

1. {1, 2, 3, 4}
2. {2, 4, 6, 8}
3. {1, 2, 3, 4, 5}
4. {8, 6, 4, 2}

Correct answer: {1, 2, 3, 4}

Solution

From x + 2y = 10 we get x = 10 - 2y. For x to lie in A = {1,...,10} (and be a natural number ≥ 1): y = 1 -> x = 8; y = 2 -> x = 6; y = 3 -> x = 4; y = 4 -> x = 2; y = 5 -> x = 0 (not in A). So R = {(8,1), (6,2), (4,3), (2,4)}. The range of R is the set of y-values: {1, 2, 3, 4}.

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