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PHL 245 S L0101 (2001):
Modern Symbolic Logic
– Test 2 (Practice) Answer Key.
Last
Name:
.
First
Name:
.
Student Number:
.
•
This document is merely intended to be a useful study aid for Test 2. The kinds of questions in this
document are
not the only kinds of questions that may be asked on the test.
Merely answering these
questions is no substitute for regular attendance in class and doing the assigned homework.
The
actual test may not resemble this document in every respect.
•
There are
many
possible correct answers for the symbolization questions – I have only indicated
one same sample answer in each case.
Part I:
SD+ Derivation
Show in
SD+
that the following sentences are inconsistent:
(B
⊃
D) & (~B
⊃
~A)
A
≡
(~B
∨
Here are two derivations:
1
(B
⊃
D) & (~B
⊃
~A)
2
3
A
≡
(~B
∨
4
~ [ (~O & ~A)
∨
2, DeM
5
~ (O
≡
A)
4, Equiv
6
A
Assumption
7
~B
∨
3,
≡
E
8
(~B
∨
D) & (~B
∨
O)
7, Dist.
9
(B
⊃
D) & (B
⊃
O)
8, Impl., 8, Impl.
10
~B
⊃
~A
11
A
⊃
B
10, Trans
12
B
⊃
O
13
B
6,11,
⊃
E
14
O
12,13,
⊃
E
15
O
Assumption
16
~B
∨
O
15,
∨
I
17
B
⊃
D
18
~ B
∨
D
17, Impl.
19
(~B
∨
D) & (~B
∨
O)
20
~B
∨
19, Dist.
21
A
3,20,
≡
E
22
O
≡
A
614, 1521,
≡
I
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View Full Document PHL 245 S L0101 (2001):
Modern Symbolic Logic
– Test 2 (Practice) Answer Key.
1
(B
⊃
D) & (~B
⊃
~A)
2
3
A
≡
(~B
∨
4
~B
⊃
~A
5
A
⊃
B
4, Trans.
6
B
⊃
D
7
A
⊃
D
56, HS
8
A
≡
(B
⊃
3, Impl.
9
A
Assumption
10
B
⊃
8,9
≡
E
11
B
5,9
⊃
E
12
10,11
⊃
E
13
O
14
15
16
~A
915,
17
(A
⊃
(~B
∨
(D & O)) & (~B
∨
(D & O)
⊃
A)
3, Equiv.
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This note was uploaded on 09/28/2009 for the course PHL 245 taught by Professor Bangu during the Summer '05 term at University of Toronto Toronto.
 Summer '05
 bangu

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