2.2.2. Tautology, Contradiction, and Contingency

Try these first

1. 1.

   What is an example of a tautology?

   Hint

   Think of a statement that covers all truth values.

2. 2.

   What is a contradiction?

   Hint

   It cannot be true under any condition.

3. 3.

   What is a tautology?

   • A proposition that is always false
   • A statement that can sometimes be true
   • A statement that is always true

   Hint

   Consider its behavior in all possible scenarios.

4. 4.

   True or False: A contradiction is sometimes true.

   • True
   • False

   Hint

   Think about a scenario where it always holds.

5. 5.

   Consider the expression p ↔ (q ∨ r). Analyze its properties and classify it as tautology, contradiction, or contingency and justify your reasoning.

   Hint

   Examine truth values for different conditions of p, q, and r.

6. 6.

   Demonstrate the truth of De Morgan's laws: ¬(p ∧ q) ≡ ¬p ∨ ¬q using a truth table and identify whether it's a tautology or a contradiction.

   Hint

   Don’t forget to check all four combinations of truth values for p and q.