CMPT 260
Assignment #1
Propositional Calculus
Due: Sept. 24, 2013
1.
For each of the following English statements, give the equivalent propositional expression. Be
sure to define all propositions used.
a.
Either x does not have the value 2 or the program will crash.
b.
An error message will be printed if a wrong value is obtained.
c.
Handling the three cases is sufficient for the program to work.
d.
I will get the program working only if I figure out this bug.
e.
To get this assignment done it is necessary and sufficient for the program to be correct
and the printer to be working.
2.
Use the precedence rules to give the fully parenthesised logical expression that is equivalent to
the following logical expression:
A
⇒
B
⇔
A
∨
¬
C
∧
B
⇒
D
∧
E.
3.
For the following expression, determine whether it is a tautology, a contradiction or a
contingent by giving its truth table
(P
⇒
Q)
∨
¬
(Q
⇒
P).
4.
Prove that
(A
⇒
¬
B)
∧
(B
⇒
A)
≡
¬
B
using the precedence rules and the laws for statement algebra. Be sure to state each rule or law
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 Winter '14
 Logic, Proposition, Propositional calculus, Conjunctive normal form, Proof theory

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