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Which of the following relations does NOT define a function?

1. f = {(x, x) | x ∈ R}
2. g = {(x, 3) | x ∈ R}
3. h = {(n, 1/n) | n ∈ I}
4. t = {(n, n²) | n ∈ N}

Correct answer: h = {(n, 1/n) | n ∈ I}

Solution

The relation h does not define a function because it is not defined for all integers; specifically, it is undefined for n = 0, which leads to a division by zero. A function must have a unique output for every input in its domain.

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