Exercise · ZW-FUNCTION-011 · ★★★ Advanced

Let \(f : \mathbb{N} \to \mathbb{N}\) with \(\mathbb{N} = \{1, 2, 3, \ldots\}\) and \(f(n) = n + 1\). Which statement is true?

Choose one option.

Show answer
  • B. It is injective but not surjective

Explanation

If \(n+1 = m+1\) then \(n = m\), so \(f\) is injective. But \(1\) has no preimage, since \(n+1 \geq 2\) for every \(n\) in \(\mathbb{N}\), so it is not surjective.

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Review the concept: Function

A function f from A to B assigns to each element of A exactly one element of B. A is the domain and B the codomain.

\[f:A\to B\]

More practice problems: function

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