Assignment2_solutions

Assignment2_solutions - MACM 101 Discrete Mathematics I...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MACM 101 Discrete Mathematics I Exercises on Predicates and Quantifiers. Due: Tuesday, October 13th (at the beginning of the class) Reminder: the work you submit must be your own. Any collabora- tion and consulting outside resourses must be explicitely mentioned on your submission. Please, use a pen. 30 points will be taken off for pencil written work. 1. Determine the truth value of each of these statements if the universe of each variable consists of (i) all real numbers, (ii) all integers. (a) x y ( x + y 6 = y + x ) (b) x y ( x + y = 2 2 x- y = 2) Solution (a) Formally negating the statement we get x y ( x + y = y + x ) , which is the law of commutativity of addition. Thus statement (a) is false in both universes, because addition is com- mutative and for any x,y we have x + y = y + x . (b) The statement is false in both universes. To prove it we need to prove that negation of this statement is true. ( x y ( x + y = 2 2 x- y = 2)) x y x + y 6 = 2 2 x- y 6 = 2) Let us assign x = 2 and then the quantified predicate turns into 2 + y 6 = 2 4- y 6 = 2 y 6 = 0 y 6 = 2 . We see that the quantified statement is true for all y and thus we have the negation of statement (b) proven. 1 2. Use predicates and quantifiers to express this statement There is a man who has visited some park in every province of Canada Solution Let V ( x,y ), where x is a person and y is a park be a predicate Person x visited park y ....
View Full Document

Page1 / 6

Assignment2_solutions - MACM 101 Discrete Mathematics I...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online