Question: 1. Construct truth tables for the following PC wff and use the tables to determine whether or not each is PC-valid: (a) p (b) ~

1. Construct truth tables for the following PC wff and use the tables to determine whether or not each is PC-valid:

(a) p

(b) ~ (p º q) É (~ p º ~ q)

(c) ~ (p ˄ (q ˄ ~ p)) ˅ r

2. Explain with reference to the Formation Rules for PC whether the following are wff:

(a) ((p ˅ p) É ((~ p ˅ ~ p) É p))

(b) (~ p ~ q)

3. Use the method of truth tables to test the following inference for validity in the propositional calculus:

Alice is annoyed unless Ben is bored Alice is annoyed if Ben is bored ⸫ If Ben isn’t bored then Alice isn’t annoyed

4. Test the following wff for validity in PC by the reduction method. Number the steps in your answers.

(a) ((p É ~ q) É r) É (q É (s É r))

(b) ~ (~ (p ˄ q) ˄ (r É q) ˄ (s ≡ r) ˄ (q ˅ s) ˄ p)

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