PHIL12A
Section answers, 14 March 2011
Julian Jonker
1
How much do you know?
1.
Use truth tables to check whether the following equivalences hold:
(a)
P
→
Q
⇔ ¬
Q
→ ¬
P
P
Q
P
→
Q
¬
Q
→ ¬
P
T
T
T
T
T
F
T
T
F
T
T
F
T
F
F
T
F
F
F
T
F
T
F
T
T
F
T
T
T
F
F
F
F
T
F
T
F
T
T
F
(b)
P
↔
Q
⇔
(
P
→
Q
)
∧
(
Q
→
P
)
P
Q
(
P
↔
Q
(
P
→
Q
)
∧
(
Q
→
P
)
T
T
T
T
T
T
T
T
T
T
T
T
T
F
T
F
F
T
F
F
F
F
T
T
F
T
F
T
T
F
T
T
F
T
F
F
F
F
F
T
F
F
T
F
T
F
T
F
2.
Translate the following arguments into the Blocks language, and then write informal proofs of
their validity. Explicitly notes any inferences using
modus ponens
, biconditional elimination, or
conditional proof.
1
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(Based on Ex 8.6)
1
a
is a large tetrahedron or a small cube.
2
b
is not small.
3
If
a
is a tetrahedron or a cube, then
b
is large or small.
4
a
is small or
b
is large.
Translation:
1
(Tet(a)
∧
Large(a))
∨
(Cube(a)
∧
Small(a))
2
¬
Small(b)
3
(Tet(a)
∨
Cube(a))
→
(Large(b)
∨
Small(b))
4
Small(a)
∨
Large(b)
By premise 1, either
a
is a large tetrahedron or a small cube. Let’s consider each case.
Case:
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 Spring '08
 FITELSON
 Logic, 2k, 2L, Julian Jonker

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