Let S be the set S = {a, b, c, d} and consider the function f : P(S) → Z given by f(X) = |X| Show that f is not one-to-one by writing down two distinct subsets X, Y ∈ P(S) that satisfy f(X) = f(Y). Write down a subset X that satisfies f(X) = 4 or explain why no such subset X exists. Write down a subset X that satisfies f(X) = 0 or explain why no such subset X exists.
Let S be the set S = {a, b, c, d} and consider the function f : P(S) → Z given by f(X) = |X| Show that f is not one-to-one by writing down two distinct subsets X, Y ∈ P(S) that satisfy f(X) = f(Y). Write down a subset X that satisfies f(X) = 4 or explain why no such subset X exists. Write down a subset X that satisfies f(X) = 0 or explain why no such subset X exists.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.1: Functions
Problem 5E: A Function f is a rule that assigns to each element x in a set A exactly ________ element(s) called...
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Let S be the set S = {a, b, c, d} and consider the function f : P(S) → Z given by f(X) = |X|
Show that f is not one-to-one by writing down two distinct subsets X, Y ∈ P(S) that satisfy f(X) = f(Y).
Write down a subset X that satisfies f(X) = 4 or explain why no such subset X exists.
Write down a subset X that satisfies f(X) = 0 or explain why no such subset X exists.
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