Let S be a subset of a universal set U. The characteristic function fs of S is the function from U to the set {0. 1) such that fs(x) = 1 if x belongs to S and fs(x) = 0 if x does not belong to S. Let A and B be sets. Show that for all x ∈ U,

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The given condition for S be a subset of universal set U.A new function is called the characteristic function fs of S is the function from U to the set {0. 1) such that fs(x) = 1 if x belongs to S and fs(x) = 0 if x does not belong to S. Let A and B be sets.