6.8.3. Equality of Dual and Original Statement

Try these first

1. 1.

   What is the dual of the statement A and B?

   Hint

   Remember to swap the 'and' with 'or'.

2. 2.

   If p is a literal, what is its dual?

   Hint

   It's a special case when dealing with single literals.

3. 3.

   What is the dual of p ∧ q?

   • p ∨ q
   • ¬p ∧ q
   • p → q

   Hint

   Look closely at the operators.

4. 4.

   If a statement is a single literal, does its dual remain the same?

   • True
   • False

   Hint

   Remember the characteristics of literals.

5. 5.

   Prove that if P and Q are logically equivalent, their duals P* and Q* are also logically equivalent.

   Hint

   Focus on the structure of the propositions and the effects of switching.

6. 6.

   Find and demonstrate the dual of a complex compound statement like A ∧ (B ∨ C). Explain your reasoning.

   Hint

   Refer to the rules of duality.