EECS 1019 Lecture Notes - Lecture 7: Empty Set, Contraposition

• School: York University
• Department: Electrical Engineering and Computer Science
• Course: EECS 1019
• Professor: John Michael Machacek

Document Summary

1. 1 #38 f) construct truth table for (p q) r p q. 1. 3 #18 determine whether ( p (p q)) q is a tautology p q p p q p (p q) q. Not a tautology ( p (p q)) q ( p ( p q)) q. 1. 4 #16 determine the truth value of x (x2 x) where x is from the domain consisting of all real numbers. Note the negation of the statement is x(x2=x) which is true by taking x=0(or x=1) 1. 5 #30 d) express y( xr(x,y) xs(x,y)) so that no negation is outside a quantifier. 1. 6 #24 a) identify the error: x(p(x) q(x)) premise, p(c) q(c) error, p(c) error, xp(x) error, q(c) error, xq(x) error, x(p(x) xq(x)) wrong. 1. 7 #16 prove that if x, y and z are integers and x+y+z is odd, then at least one of x, y or z is odd. Assume that not t least one of x, y or z is odd.