2.4. Verification of Logical Identities

Try these first

1. 1.

   Give an example of a tautology.

   Hint

   Think of statements that are always true.

2. 2.

   What is a contradiction?

   Hint

   Consider statements that can never be true.

3. 3.

   What does a tautology always represent?

   • Always true
   • Always false
   • Sometimes true

   Hint

   Think of statements that never fail.

4. 4.

   Is p ∧ ¬p a tautology?

   • True
   • False

   Hint

   Consider if a statement can be both true and false.

5. 5.

   Using logical identities, prove that (p ∨ q) ∧ ¬(p ∧ q) is logically equivalent to p ⊕ q (exclusive or).

   Hint

   Look for substitutions in common logical identities.

6. 6.

   Construct a truth table for p ∨ (q ∧ r) and simplify it using logical identities.

   Hint

   Consider breaking down into basic components for clarity.