2.3.1. Identity and Double Negation Laws

Try these first

1. 1.

   What is a tautology?

   Hint

   Think of statements involving 'or' conditions.

2. 2.

   What is the double negation law?

   Hint

   Consider how negating works.

3. 3.

   What does a tautology signify in logic?

   • Always true
   • Always false
   • Sometimes true

   Hint

   Think of it as a universal truth in logical terms.

4. 4.

   Is p and ¬p a contradiction?

   • True
   • False

   Hint

   Reflect on the nature of opposing statements.

5. 5.

   Show that the two expressions (p ∨ q) ∧ (¬p ∨ r) and r ∨ q are logically equivalent using simplifications.

   Hint

   Start by distributing the components of the first expression.

6. 6.

   Prove that if (p → q) ≡ (¬q → ¬p) is always true, then demonstrate using a truth table.

   Hint

   Outline the truth values for p and q to reveal their corresponding outcomes.