CS 336 PreTest 1 Solutions
Logic
1. Sentential Calculus (SC)
1.1* Prove that for all propositions
p
,
q
, and
r
:
a)
[~q
⇒
~p]
[p
q]
Consider the following truth table:
p
q
~
q
~
p
~
~
q
p
⇒
p
q
⇒
[~
~
]
[
]
q
p
p
q
⇒
⇒
⇒
F
F
T
T
T
T
T
F
T
F
T
T
T
T
T
F
T
F
F
F
T
T
T
F
F
T
T
T
b)
[p
(q
∧
r)]
[~p
∨
(q
r)]
Consider the following truth table:
p
q
r
q
r
∧
(
)
p
q
r
⇒
∧
~
p
~
p
q
r
∨
∨
[
(
)]
[~
]
p
q
r
p
q
r
⇒
∧
⇒
∨ ∨
F
F
F
F
T
T
T
T
F
F
T
F
T
T
T
T
F
T
F
F
T
T
T
T
F
T
T
T
T
T
T
T
T
F
F
F
F
F
F
T
T
F
T
F
T
F
T
T
T
T
F
F
T
F
T
T
T
T
T
T
T
F
T
T
2. First Order Predicate Calculus (PC)
2.1.* State an assertion that, if true, would falsify each of the following claims:
a)
All zamzows have tenockritus.
“A is a zamzow but does not have tenockritus.”
b)
Some zamzows have tenockritus.
“There exist no zamzow that has tenockritus.”
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View Full Document2.2. Given the following two axioms:
2200
x Px
⇒
Qx
5
x ~Qx
∧
~Rx
Prove that
y ~Py
From the second assumption we have some element
a
so that
~
~
Qa
Rx
∧
. This
implies that
~
Qa
. If Pa were true then from the first assumption we could
conclude
Qa
, but that contradicts
~
Qa
.
We coclude that
~
Pa , and thus
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 Fall '08
 Myers
 Predicate logic, Universal quantification, Firstorder logic, following truth table, Mary y, ∃y CHILDOF xy

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