21127 Study Guide - Midterm Guide: Negation, European Route E6, Natural Number
16 Dec 2015
School
Department
Course
Professor
Document Summary
Exam 1 (1) consider the universal context to be u = z. Let p (x) be the proposition 1 x 3 . Let q(x) be the proposition k z. x = 2k . Let r(x) be the proposition x2 = 4 . Let s(x) be the proposition x = 1 . Y z. x (cid:54)= y p (x) r(y: x z. Y z. (s(x) q(x)) p (y) q(y: x z. S(x) p (x) q(x: x z. S(x) p (x) q(x) (2) for each of the following claims, de ne some sets and variable propositions to express the claim in concise symbolic, logical notation. For each of the following statements, decide whether it is true or false. Note: none of the answers are it depends . X r. y r. x2 y2 0 (5) prove or disprove the following claim rigorously: Z n {0}. ((x y) = z) ((y x) = z) X, y r. 2xy x2 + y2.
