PHIL12A
Section questions, 13 April 2011
Julian Jonker
1
How much do you know?
1.
Translate the following sentences into FOL twice, using universal quantifiers for one translation and
existential quantifiers for the other.
(a)
Every cube is left of every tetrahedron.
∀
x
∀
y(Cube(x)
∧
Tet(y)
→
LeftOf(x,y))
(b)
Some cube is left of some tetrahedron.
∃
x
∃
y(Cube(x)
∧
Tet(y)
∧
LeftOf(x,y))
(c)
No cube is left of any tetrahedron.
∀
x
∀
y((Cube(x)
∧
Tet(y))
→ ¬
LeftOf(x,y))
(d)
Some cube is not left of some tetrahedron.
The following might be okay, especially given that this part of the course was dealing with multiple quan
tifiers of the same type:
∃
x
∃
y(Cube(x)
∧
Tet(y)
∧ ¬
LeftOf(x,y))
But really the sentence is saying that there is a cube which is not left of any tetrahedron. Translate that as
follows:
∃
x(Cube(x)
∧ ∀
y(Tet(y)
→ ¬
LeftOf(x,y)))
2.
Carefully translate the following sentences.
(a)
There is a pair of small cubes.
∃
x
∃
y(x
6
=
y
∧
Cube(x)
∧
Small(x)
∧
Cube(y)
∧
Small(y))
(b)
There is a cube to the left of some cube.
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 Spring '08
 FITELSON
 Polyhedron, Platonic solid, Tetrahedron, rectification, Polyhedral compound

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