MAT102H5 Study Guide - Final Guide: Contraposition, Natural Number
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MAT102H5 Full Course Notes
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Given a real number x, let a be the phrase 1. 2 , b the phrase x z , c be the the phrase x2 = 1 , and d the phrase x = 2 . 2 < x < 5 (a) a c. Since we cannot guarantee a to be true, and by that we can say that this is a true statement. (b) (a b) c. Since we cannot guarantee a b to be true, and by that we can say that this is a true statement. (c) d [a b ( c)] This is due to the concept of vacuous truths. Since we cannot guarantee d to be true, and by that we can say that this is a true statement. For each statement, write the meaning in english and decide whether it is true or false (x and y represent real numbers). Explain your decision brie y. (a) x y(x y)