Let A,B be non-empty subsets of mathbb N with cardinality Age2. Let S1=f:Ato Bmid f is one-to-onequadandquad S2=g:Bto Amid g is onto. Which of the following statements is true?

(C) If B=mathbb N and A is finite, then there exists a one-to-one map from B to S1.

Q23Section B (Part B)23 of 120

Cardinality of sets of injections and surjections

Let $A,B$ be non-empty subsets of $\mathbb N$ with cardinality $|A|\ge2$ . Let

$S_1=\{f:A\to B\mid f\text{ is one-to-one}\}\quad\text{and}\quad S_2=\{g:B\to A\mid g\text{ is onto}\}.$

Which of the following statements is true?

Pick an option to check your answer.

Keyboard: A–D answer · S solution · ←/→ previous/next