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COT 3100H Spring 2008 Homework #1
Assigned: 1/8/08
Due: 1/15/08
1) Write out a truth table for the following logical expressions:
a)
q
q
p
p
→
→
∧
)]
(
[
b)
)
(
)]
(
)
[(
r
p
r
q
q
p
→
→
→
∧
→
c)
))
(
(
r
p
q
p
∨
¬
∧
¬
∧
2) Determine all truth value assignments for the primitive statements p, q, r, s, t that make
the following expression false:
)
(
]
)
[(
t
s
r
q
p
∨
→
∧
∧
.
3) Negate the following boolean expression and simplify the result as much as possible.
Please show each step and name the rule you are using at each step:
)
(
r
q
p
q
p
∧
¬
∧
¬
∨
∨
4) Show that the following two logical expressions are equivalent using the laws of logic:
)]
(
[
)
(
q
r
q
q
p
¬
∨
∧
¬
∧
→
and
)
(
p
q
∨
¬
5) Prove the following logical argument using the rules of implication. Please show each
step and state which rule you use.
r
q
p
→
∨
¬
)
(
)
(
t
s
r
∨
→
u
s
¬
∧
¬
t
u
¬
→
¬

p
∴
6) Create simple statements for p, q, r, s, t and u for problem number 5 above that make
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 Spring '09

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