Symbolic Logic including constructing proofs using various rules

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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 Ú C), (S . (T ? W)), ~ (~ Y ? W), ~ B = ~ (C Ú T)
/ ~ (B Ú Y)
b. (A . F) ? (C Ú G), ~ (C Ú (F . G)), F = ~ (X . Y), ~ (X Ú ~ W)
/ ~ (A Ú X)
c. Q = ~ (A Ú B), P ? ~ (Q Ú ~ T), ~ (S ? ~ W), (Q ? X) ? ~ (S . W)
/ ~ (P Ú B) . ~ (X v A)
[Extra credit]
d. (W Ú T) ? ~ A, ~ (X ? S), ~ (T Ú S) ? ~ X, C ? (P . S),
(D ? (C . E)) = X / ~ ((C v D) Ú (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 Ú C), C = (E . F), ~ (F Ú B) / ~ A
b. A ? ~ (X . Y), B = (D Ú ~ F), ~ (D Ú W), F = ~ Y / (A . B) ? ~ X
c. ~ A ? (E ? (B Ú C)), S = ~ (D Ú C), T ? (S . ~ B), ~ A Ú C
/ T ? ~ (D Ú E)
[Extra credit]
d. (~ C . (F Ú E)) Ú (C . ~ (F Ú 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 Ú r)) ? (~ (p ? ~ s) ? ~ q)
b. p = (p . (q Ú ~ q))
c. ((p ? q) . (q ? r)) Ú (r ? p)
[Extra credit]
d. ((p Ú 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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