21127 Study Guide - Quiz Guide: Edison Electric Institute, Natural Number, Contraposition
16 Dec 2015
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Collaborators: the ghosts of bertrand russell and paul erd os: proof or spoof ? (10 pts) Let a and b be any two subsets of a set u . We claim (a b) (a b) (a b) (b a) We will prove this by contrapositive, so we want to show, for every x u , that x / (a b) (b a) = x / (a b) (a b) Afsoc that x (a b) (b a). Then (x a x / b) (x b x / a) so we have two cases. Case 1: if x a x / b then certainly x a b and x / a b. Case 2: if x b x / a then certainly x a b and x / a b. Thus, x (a b) (a b), since this holds in either case. This proof does not actually accomplish what it claims. The writer expresses the subset relationship as a conditional statement.
