Let S be a set and let A be a subset of S. The characteristic function of A is a
Chapter 5, Problem 41(choose chapter or problem)
Let S be a set and let A be a subset of S. The characteristic function of A is a function cA: S S 50, 16 with cA(x) = 1 exactly when x [ A. a. Let S = 51, 2, 3, 4, 56 and A = 51, 3, 56. Give the ordered pairs that belong to cA. b. Prove that for any set S and any subsets A and B of S, cA d B(x) = cA(x) # cB(x). 406 Relations, Functions, and Matrices Section 5.4 Functions 407 c. Prove that cA(x) = 1 cA(x). d. Is it true that for any set S and any subsets A and B of S, cA c B(x) = cA(x) + cB(x)? Prove or give a counterexample.
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