CSE4/586 (Spring 2010): Homework 1
1. (70 points)
Let
P
,
Q
,
R
range over state predicates of some program. Prove or disprove
the following:
1. [
P
∨
(
P
∧
Q
)
≡
P
]
2. [
P
∧
(
Q
∨
R
)
≡
(
P
∧
Q
)
∨
(
P
∧
R
) ]
3. [
P
∨
(
Q
∧
R
)
≡
(
P
∨
Q
)
∧
(
P
∨
R
) ]
4. [
¬
(
P
∧
Q
)
≡ ¬
P
∨¬
Q
] (De Morgan)
5. [
¬
(
P
∨
Q
)
≡ ¬
P
∧¬
Q
] (De Morgan)
6. [
P
⇒
Q
≡ ¬
P
∨
Q
]
7. [ (
P
n≡
Q
)
≡
(
Q
n≡
P
) ]
2. (30 points)
Translate the following English statements into predicate logic:
1. Every positive integer is smaller than the absolute value of some negative integer. (Use
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 Spring '09
 Negative and nonnegative numbers, following English statements, ¬P ¬Q

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