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Math 2534 Test 1 Solutions Spring 2008
Problem 1: (8pts) Given the following statements:
p: Mary is a Math major
q: James is a CS major
r: Karla is an Engineer
w: Harry is a Hokie
Given the statement: ()()p qrw¬?¬ ? ? is false and p is false, determine if r, p, q, and
w are true or false and justify your reasoning.
Solutions: We know the implication ( ) ( )p qrw¬ ?¬ ? ? is false and p is also false.
We also know that ( )p q¬?¬ must be true and ( )rw? must be false in order for the
implication to be false. Since the "or" statement ( )p q¬ ?¬ is true and p is false, then we
know that is true but and q can not be derermined. pq¬¬ Since ( )rw? is false and is
an "or" statement then r and w are both false.
Problem 2: (8pts) Express the following sentences in symbolic logic using multiple
quantifiers. Specify domains for each variable used and define a predicate P(x,y)
a) Most people like some fast food restaurants.
b) Each of us has a favorit...

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