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(Solved): Suppose S is a set and A is a subset of S. DEFINITION 1.1. The characteristic function of a subset ...



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Suppose is a set and is a subset of . DEFINITION 1.1. The characteristic function of a subset of is the function so that (a) Consider the characteristic function for the subset of the set . Draw a Venn diagram for , labelling the following sets: - - - . (b) Let be a set and suppose is a function: prove that it is the characteristic function of some subset of , i.e. there exists some subset such that .


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