21127 Study Guide - Quiz Guide: Book Of Ezekiel, Contraposition, Burh
16 Dec 2015
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Prove that x r. x2 (cid:54)= 1 x (cid:54)= 1. Look at how weird/di cult it is to prove this directly, but look at how easy it is to prove by contrapositive! Suppose x r and suppose x = 1. Prove each of the following claims. (cid:92) (cid:92) x p arbitrary x p , we know 0 (cid:84) x p sx. x n. P = {y r | y > 0} Sx = {y r | 1 y 1} Let x p be arbitrary and xed. Observe that x < 0 < x, so x 0 x. Next, we want to show there are no other elements of this set. Let y r and suppose y (cid:54)= 0. We want to show y is not an element of the set. In either case, we have found that y is not an element of (at least) one of the sets in the intersection.
