2.2.3. Logically Equivalent Statements

Try these first

1. 1.

   What is a tautology?

   Hint

   Think about statements that can't be false.

2. 2.

   Give an example of a contradiction.

   Hint

   Consider combinations that make both statements false.

3. 3.

   What type of statement is always true?

   • Tautology
   • Contradiction
   • Contingency

   Hint

   Consider statements that cannot be false.

4. 4.

   A statement that is always false is called a?

   • True
   • False

   Hint

   Think of combinations that cannot hold true.

5. 5.

   Show using logical identities that '¬(p ∧ q) ∧ (¬p ∨ r)' can be simplified. Prove it results in an equivalent expression.

   Hint

   Think about how negation affects conjunctions.

6. 6.

   Given p → q and r → s, prove that 'p ∧ r → q ∧ s' is logically equivalent using logical identities.

   Hint

   Consider the implications separately and how they relate.