CSE 20: Discrete Mathematics
Fall 2011
Problem Set 3
Instructor: Daniele Micciancio
Due on:
Wed. Oct. 19, 2011
Problem 1 (8 points)
Let the following predicates be given. The domain is that of all books.
•
B(x) = “x is boring”
•
H(x) = “x is a historical essay”
•
E(x) = “x is expensive”
•
M(x,y) = “x is more interesting than y”
(a)
Write the following statements in predicate logic
1. All historical essays are boring
2. There are some boring books that are not historical essays
3. All boring historical essays are expensive
(b)
Write the following predicate logic statement in everyday English.
Don’t give just a wordforword
translation; your sentence should make sense.
∀
x.
[
H
(
x
)
→ ∃
y.
(
¬
E
(
y
)
∧
M
(
y, x
))]
(c)
Formally negate the statement from part (b). Simplify your negated statement so that no quantifier lies
within the scope of a negation.
Problem 2 (9 points)
In this problem, all variables range over the set of all integers. Recall that the relation
a

b
(read “a divides
b”) is defined as
a

b
≡
“
∃
c.b
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 Spring '08
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 Prime number, Daniele Micciancio

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