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PHIL1012 Introductory Logic   ·   Problem Set 3   ·   Week 5

1. Use a truth table to test whether the following argument is valid. (Present the truth table, and say whether the argument is valid or invalid. When presenting your truth table you must fill in the truth values in the matrix in the way presented in lecture and in §3.3 of the textbook where it says “Here is a trick for filling in the truth values in the matrix”.) If the argument is invalid, give a counterexample.

(¬A → ¬C)

((C ∨ ¬A) ↔ E)

∴ (E ∧ ¬C)

2. Say whether or not the following argument:

(¬B ↔ (¬A ∨ ¬¬(A → B)))

¬(A → B)

∴ ¬(¬A ∧ ¬¬B)

is an instance of the following argument form:

(α ↔ (β ∨ ¬γ))

γ

∴ ¬(β ∧ ¬α)

If you say it is an instance, then also say what substitutions of propositions for wff variables have to be made to obtain the argument from the argument form. If you say it is not an instance, explain why.