1. Let \( A \) and \( B \) be two finite sets. Justify the following statements.(a) If \( f: A \rightarrow B \) is an injection, then \( |A| \leq |B| \). (Consider the Pigeonhole Principle.)(b) If \( f: A \rightarrow B \) is a surjection, then there is an injection \( g: B \rightarrow A \), and deduce from the first part that \( |B| \leq |A| \).

To prove if f: A→B is injective then A≤B It is sufficient to prove that if A>B then f is not…

Answered: 1. Let A and B be two finite sets.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. Let A and B be two finite sets. Justify the following statements. (a) If f: A B is an injection, then |A|≤|B|. (Consider the Pigeonhole Principle.) (b) If f: AB is a surjection, then there is an injection g: BA, and deduce from the first part that B|≤|A|.