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|.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
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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: A → B is a surjection, then there is an injection g: B → A, and deduce from the first part
that |B| ≤ |A|.
Transcribed Image Text: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: A → B is a surjection, then there is an injection g: B → A, and deduce from the first part that |B| ≤ |A|.
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