1. Show that the De Morgans laws are correct, employing truth tables.

2. Simplify:

(p ? p) ? (p ? q)

3. Using equivalence laws, demonstrate that the given formula is a tautology: p ? (p ? (p ? q))

4. Show that the formula is satisfiable using a semantic tableau. (p ? q) ? (p ? q)

?? ? ? ? =1 =1

5. Prove:

This expression generalizes the first part of the De Morgans law, (p ? q) ? p ? q. To prove it, use mathematical induction on n.