EECS 1019 Study Guide - Midterm Guide: First-Order Logic, Irrational Number, Contraposition

• School: York University
• Department: Electrical Engineering and Computer Science
• Course: EECS 1019
• Professor: Suprakash Datta

Document Summary

Winter 2017 - solutions instructor: s. datta: (6 points) let g : z z z z be de ned by g(x, y) = (2x, x + y). Recall that to prove that a function is injective, we must show that if f (x, y) = f (z, w) then (x, y) = (z, w). The function is not onto because it will not produce any pair whose rst number is odd, e. g. (1, 1): (3 points) prove or disprove: if x is an irrational number, then x is an irrational number. Solution: the easiest approach is proving the contrapositive. The contrapositive is: if x is a rational number, then x is a rational number. So x = m n for some m, n z, n > 0. 2 and thus rational since it is a fraction. 2 n: (2+2 points) write down the following statement in predicate logic (using quanti ers).