1. Using a truth table show that two propositions (p q) (~p q),

   and

   p q

note: = exclusive disjunction symbol.

1. are not equivalent. (i.e show that (p q) (~p q) = p q

2. Using equivalence laws of propositional logic, show that (p q) (p q)

   is a tautology

3. Using equivalence laws of propositional logic, show that ~(p v (~p ^ q)) ~p ^ ~q

4. Using equivalence laws of propositional logic, show that (p q r) (p q ~r) p ~r