CMPSC360hw1soln

# CMPSC360hw1soln - CMPSC 360 Discrete Mathematics for...

This preview shows pages 1–2. Sign up to view the full content.

CMPSC 360 Discrete Mathematics for Computer Science, Fall 2008 Homework 1 Solutions Out: Aug. 27, Due: Sept. 4 by 5:00pm Note: These solutions are not necessarily the model answers. Instead, they are tutorial in nature and may contain a little more explanation than an ideal solution. Also, there may be more than one correction solution. 1. [Classical logic] [30 pts, 2 pts each in (a) and (b), 6 pts for (c)] (a) Writing sentences as quantiﬁed propositions: (I) “No one, who is going to a party, ever fails to brush his or her hair.” x,P ( x ) B ( x ) . (II) “No one looks fascinating, if he or she is untidy.” x,U ( x ) ⇒ ¬ F ( x ) . (III) “Opium-eaters have no self-command.” x,O ( x ) N ( x ) . (IV) “Everyone who has brushed his or her hair looks fascinating.” The word everyone indicates that the statement is universal. Also the act of brushing her or his hair is suﬃcient for one to look fascinating. Thus we have x,B ( x ) F ( x ) . (V) “No one wears kid gloves, unless he or she is going to a party.” This statement means that “A person wears kids gloves only if he or she is going to a party”. Thus we have x,K ( x ) P ( x ) . (VI) “A person is always untidy if he or she has no self-command.” This statement is the same as “If a person has no self-command, then he/she is always untidy”. The corresponding quantiﬁed proposition is x,N ( x ) U ( x ) . (b) Writing the contrapositives:

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 10/08/2008 for the course CMPSC 360 taught by Professor Haullgren during the Fall '08 term at Penn State.

### Page1 / 3

CMPSC360hw1soln - CMPSC 360 Discrete Mathematics for...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online