UNIVERSITY OF WATERLOO
School of Computer Science
CS245
Logic and Computation
Spring 2009
ASSIGNMENT 1
(Due: Thursday, May 21, 2009 at 5:00pm)
Use
makeCover
to produce a cover page for your assignment and hand in your assignment in the CS245
assignment box. Assignments are to be done individually.
1. (2 marks) Insert brackets into the following formulae so that we do not have to rely on the associativity
and order of precedence of the logical connectives to understand the formulae.
(a)
p
⇔
q
⇔ ¬
p
⇒ ¬
q
⇔
p
(b)
a
⇒
b
∧
c
∧
d
∨
e
2. (3 marks) Assuming standard rules of precedence and associativity, are the following wellformed for
mulae? If not, explain why not.
(a)
p
⇒
q
¬
r
(b)
¬
p
⇒ ¬
q
(c)
p
¬ ⇒ ¬
q
3. (6 marks) Express the following sentences as propositional formulas.
Show the English phrase that
your propositional symbols represent (e.g.,
p
– “it is raining”).
(a) When it rains it pours.
(b) If you believe it, it will happen.
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.
 Spring '08
 WORMER
 Computer Science, Logic, Logical connective, propositional formulas

Click to edit the document details