CSCI561
Fall 2010
Macskassy
Homework 3
Due Nov. 3, 2010
Student name: _____________________________
Student ID: _________________
Question 1
[Q1: 20 points]
a). P
Q is defined as being equivalent to (P
⇒
Q) ^ (Q
⇒
P). Based on this definition,
show that P
Q is logically equivalent to (P v Q)
⇒
(P ^ Q).
i) [5pts] By using truth tables.
ii) [5pts] By using the following identities:
¬ (¬P) = P
(P
⇒
Q) = (¬P v Q)
the contrapositive law: (P
⇒
Q) = (¬Q
⇒
¬P)
deMorgan's law: ¬ (P v Q) = (¬P ^ ¬Q) and ¬ (P ^ Q) = (¬P v ¬Q)
the commutative laws: (P ^ Q) = (Q ^ P) and (P v Q) = (Q v P)
the associative law: ((P ^ Q) ^ R) = (P ^ (Q ^ R))
the associative law: ((P v Q) v R) = (P v (Q v R))
the distributive law: P v (Q ^ R)) = (P v Q) ^ (P v R)
the distributive law: P ^ (Q v R)) = (P ^ Q) v (P ^ R)
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CSCI561
Fall 2010
Macskassy
Homework 3
Due Nov. 3, 2010
Student name: _____________________________
Student ID: _________________
Question 1 (cont.)
[Q1: 20 points]
b) Consider the following propositional knowledge base:
If April is whistling, then April is happy.
If the house is clean, then April is happy.
April is not happy.
i
) Use PROPOSITIONAL RESOLUTION to prove that “the house is not clean
and April is not
whistling”. Use W =
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 '09
 Moradi
 Logic, student id, Firstorder logic, CSCI561 Fall

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