Which of the following statements are true?
I. A function from a finite set to itself is one-one exactly when it is onto.
II. $f : \mathbb{N} \to \mathbb{N}$ , $f(n) = n + 1$ , is one-one and onto.
III. A bijection from $A$ to $B$ exists only if $A$ and $B$ have the same number of elements, when both are finite.
IV. Every onto function from a 3-element set to a 2-element set is one-one.

I, II and III onlyCorrect answerYour answerI, III and IV onlyCorrect answerYour answerIII onlyCorrect answerYour answerI and III onlyCorrect answerYour answer

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CorrectNot quiteAnswer D

Correct answer: D

I and III are true. II is false: nothing maps to 1, so it is not onto.
IV is false: 3 elements sharing 2 images must repeat one.

Worth noting

II fails at 1: $n + 1 \ge 2$ for every natural $n$ .

Concept: Facts about onto functions
Typical timeTypical: 150 s
Your timeYours: —

The rule this testsOnto and bijective functions

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Ten questions from Relations & Functions, at your own pace.

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