constructing proofs assignment, Philosophy Assignment Homework Help

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PHIL111 – 940 – ASSIGNMENT #4 (Units 8-9) [total =10 marks + 3 marks extra credit!] 1. Construct proofs for the following, without using C.P. or I.P. (= Unit 8) [1 mark each]. a. S ≡ ~ (D ∨ C), (S . (T ⊃  W)), ~ (~ Y ⊃  W), ~ B ≡ ~ (C ∨ T) /∴ ~ (B ∨ Y) b. (A . F) ⊃ (C ∨ G), ~ (C ∨ (F . G)), F ≡ ~ (X . Y), ~ (X ∨ ~ W) /∴ ~ (A ∨ X) c. Q ≡ ~ (A ∨ B), P ⊃ ~ (Q ∨ ~ T), ~ (S ⊃ ~ W), (Q ⊃ X) ⊃ ~ (S . W) /∴ ~ (P ∨ B) . ~ (X v A) [Extra credit] d. (W ∨ T) ⊃ ~ A, ~ (X ⊃  S), ~ (T ∨ S) ⊃ ~ X, C ⊃ (P . S), (D ⊃ (C . E)) ≡ X /∴ ~ ((C v D) ∨ (A v S)) 2. Use C.P. or I.P. or both to construct proofs for the following (= Unit 9) [1 mark each]. a. A ⊃ (B ∨ C), C ≡ (E . F), ~ (F ∨ B) /∴ ~ A b. A ⊃ ~ (X . Y), B ≡ (D ∨ ~ F), ~ (D ∨ W), F ≡ ~ Y /∴ (A . B) ⊃ ~ X c. ~ A ⊃ (E ⊃ (B ∨ C)), S ≡ ~ (D ∨ C), T ⊃ (S . ~ B), ~ A ∨ C /∴ T ⊃ ~ (D ∨ E) [Extra credit] d. (~ C . (F ∨ E)) ∨ (C . ~ (F ∨ E)), F ⊃ ~ B, (A ⊃ ~ C) ≡ ~ (X ⊃ E) /∴ B ⊃ C   1   3. Construct proofs for the following theorems (= Unit 9) [1 mark each]. a. (~ (p . q) ≡ (s ∨ r)) ⊃ (~ (p ⊃ ~ s) ⊃ ~ q) b. p ≡ (p . (q ∨ ~ q)) c. ((p ⊃  q) . (q ⊃  r)) ∨ (r ⊃  p) [Extra credit] d. ((p ∨ q) ⊃ (r . ~ s)) ⊃ (s ⊃ ((t . w) ⊃ ~ p)) 4. Symbolise and construct proof for the following argument, providing the dictionary for each (fully-written) simple sentence. No abbreviations for simple sentences will be accepted! [1 mark]. If the cat is ill, either she was fighting or ate too many mice. She was fighting only if she was attacked, and she was attacked only if either the large Siamese or the small Beagle was out. The large Siamese was out only if it was sunny, and the small Beagle was out only if it was warm. It was neither warm nor sunny, but the cat is ill. Therefore, she ate too many mice.   2   ...
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Tutor Answer

Cess
School: Rice University

Running Head: LOGICS ASSIGNMENT

1

Logics Assignment PHIL 111 – 940
Author
Institution

LOGICS ASSIGNMENT

2
Question 1a

1.S≡ ̴ (D˅C)
2.S≡ ̴ D ˅ ̴ C
3. ̴ D
4. ̴ C
5. S.(T⊃ W)≡ (S˅T) ⊃ (S˅W)
6.

(D˅T) ⊃ ( C˅T)

7.

(D˅T) ⊃B

distributive
( 3,4)
̴ B (C˅R)

since

8. S˅W ≡(D˅W)
9. D ˅ ̴ Y

(2)
since ̴ (̴ Y⊃W)

̴ (B˅Y)

(7,11)

Question 1 b
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.

(A.F) ⊃( C ˅ G)
̴ (C˅(F.G)
A˅F⊃C˅G
F≡ ̴ (X.Y)
̴ (X˅ ̴ W)
̴ X˅W
W
F≡ X
̴ ˅ Y̴
X
̴

̴(C ˅ (X.G)
̴ (G ˅ X.G)
̴(A˅X)

distributive law

5
4
8
8
2
3
2,3

Question 1c
1. Q ≡ (̴ A ˅ B)
2. P≡ ̴ ( Q ˅ ̴ T)
3. ̴ (S⊃ ̴ W)
4. ̴ S⊃ W)
5. (Q ⊃ X) ⊃ ( S.W)

3

LOGICS ASSIGNMENT
6.
7.
8.
9.
10.

3

(Q⊃X) ⊃ ̴(S ˅W)
(Q⊃X) ⊃( ̴ S˅ ̴W)
̴ (A˅B) ⊃ X⊃ ̴S˅ ̴ W
̴ (A˅B) ⊃X⊃ W˅ ̴ W
̴Q⊃X⊃ ̴S
(P˅B).(X˅A)

6
1
3
4
7,8

Question 1d
1.
2.
3.
4.
5.
6.
7.
8.

(W ˅ T) ⊃ ̴ A
̴X ⊃ S
̴(T ˅ S) ⊃ ̴X
C⊃(P.S) → C ⊃ (P˅S)
D⊃(C.E)...

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