McMaster University
Department of Computing and Software
Dr. W. Kahl
COMP SCI 1FC3
Exercise Sheet 4
COMP SCI 1FC3 — Mathematics for Computing
1February 2009
Exercise 4.1 — Predicates, formal and English
Translate each of these formulae into an English statement that expresses a mathematical fact. The domain in each
case consists of all real numbers.
(a)
∃
x
∀
y
(
x
+
y
=
y
)
(b)
∃
x
∀
y
(
xy
=
y
)
(c)
∃
x
∀
y
(
yx
=
y
)
(d)
∃
x
∀
y
(
yx
=
x
)
(e)
∀
x
∀
y
(((
x
≥ 0) ∧ (
y
≤ 0)) → (
x

y
> 0))
(f)
∃
x
∃
y
(((
x
≤ 0) ∧ (
y
≤ 0)) ∧ (
x

y
> 0))
(g)
∀
x
∀
y
((
x
=
/ 0) ∧ (
y
=
/ 0) ↔ (
xy
=
/ 0))
(h)
∀
x
∀
y
∃
z
(
x
+
y
=
z
)
Exercise 4.2 — Predicates, formal and English
Use quantifiers and predicates with more than one variable to express each of the following statements.
(a)
There is a student in this class who speaks Hindi.
(b)
Every student in this class plays some sport.
(c)
Some student in this class has visited Alaska but has not visited Hawaii.
(d)
Exactly one student in this class has visited Hawaii.
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 Spring '11
 kahl
 COMP SCI 1FC3, SCI 1FC3 Exercise

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