Answer to Question #313804 in Discrete Mathematics for Donnel

Question

Construct a truth table (truth matrix) for each of these compound proposition

1. p ∧ ~q
2. p → ~q
3. ( p ∨ q ) → ( p ∧ q)
4. ( p ∨ q ) → r
5. ( p ∨ q )∧ ~r

by using truth table (truth matrix), show that each statement is a tautology, contradictory or a contingent statement.

1. ~p ∧ q
2. ~(p ∨ q) → q
3. ~(~p ∧ q) ∨ q
4. ~p → (p → q)
5. ~p → (p ∨ q)

Answer 1

1 p ∧ ~q

2 p → ~q

3 ( p ∨ q ) → ( p ∧ q)

4 ( p ∨ q ) → r

5 ( p ∨ q )∧ ~r

1 ~p ∧ q

2 ~(p ∨ q) → q

3 ~(~p ∧ q) ∨ q

4 ~p → (p → q)

5 ~p → (p ∨ q)