CS 173: Discrete Structures, Spring 2010
Homework 2
This homework contains 6 problems worth a total of 50 points. It is due on Friday, Febru
ary 5th at 4pm.
(As usual, put your homework in the appropriate dropbox in the Siebel
basement.)
1.
[9 points] Logic notation
Translate the following sentences into propositional or predicate logic. Use the short
hand symbols (e.g.
∨
) and define the meaning of each of your predicates and proposi
tional variables. (See pages 11 and 4243 of Rosen for examples.) Be sure to include
a domain (aka replacement set) for each quantified variable. You may need to rewrite
the sentences slightly so as to make a variable more explicit.
(a) Every cookie that contains lots of butter is tasty but is also fattening.
(b) Either the tablecloth is pink, or the tablecloth is white and the red light is shining
on it.
(c) Exactly one integer is equal to its own negation.
For example, the sentence “Every car that is driven in Berkeley is a hybrid or runs on
biodiesel.” might be rendered as
∀
x
∈
C,D
(
x
)
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 Spring '08
 Erickson
 Logic, Natural number, following logical equivalences, following claim

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