Suppose that f is a function from A to B where A and B are

Chapter 2, Problem 14E

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QUESTION:

Suppose that f is a function from A to B where A and B are finite sets. Explain why | f(S )| ? | S | for all subsets S of A.

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QUESTION:

Suppose that f is a function from A to B where A and B are finite sets. Explain why | f(S )| ? | S | for all subsets S of A.

ANSWER:

SolutionStep 1Proof by ContradictionLet us assume that S be a subset of A.By Contradiction, |f[S]| > |S|Now we have to define a function x : f(S) S by x(b) = some a belong to x like

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