COT- Logic for computer science

1. Let p, q, r, and s be propositional variables. Which of the following expressions would not be correct formulas of propositional logic? Why? (a) p p p (b) p q r (c) p q (d) p (e) p p q (f) p q p (g) p q (h) pq (i) (j) p q r s

2. Consider the propositions p: John studies Logic q: John understands propositional calculus.

Translate the following formulas into expressions of the natural language: (a) p (b) p q (c) p q (d) p q (e) p q

3. Construct the truth table for (p q) p

4. Is the formula of Question 3, (p q) p, a tautology, satisfiable, or contradictory?

5. Show that the formula (pq) (p q) is a tautology.

6. Show that the formula p q and the formula (p q) are logically equivalent.