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)  

(c) ~ p ˄ p (d) ~ ((p É q) É (q ˅ r)) ˅ (p ˅ r)


[Note: The wff in (b) is a negated many-termed conjunction.]

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