2.5. Example of Logical Equivalence Proof

Try these first

1. 1.

   Define tautology and provide an example.

   Hint

   Think of an expression that yields true regardless of p’s value.

2. 2.

   What does logical equivalence mean?

   Hint

   Consider statements with identical outcomes.

3. 3.

   What is the definition of logical equivalence?

   Hint

   Think about identical outcomes in different expressions.

4. 4.

   A statement that is always true is called a?

   • Contradiction
   • Tautology
   • Contingency
   • None of these

   Hint

   Consider an example that never changes its outcome.

5. 5.

   Prove that (p ∧ q) → r is logically equivalent to ¬(p ∧ q) ∨ r using logical identities.

   Hint

   Break down the statement systematically, applying identities.

6. 6.

   Show that ¬(p ∨ q) is equivalent to ¬p ∧ ¬q, using De Morgan's Law.

   Hint

   Negation is key in switching from disjunction to conjunction.