6.8.2. Constructing Duals

Try these first

1. 1.

   What is the dual of the proposition p ∧ q?

   Hint

   Remember to switch ANDs with ORs.

2. 2.

   Construct the dual for p ∨ q.

   Hint

   Think about the dual transformation.

3. 3.

   What is the dual of the expression p ∧ (q ∨ r)?

   • p ∨ (q ∧ r)
   • p ∧ r
   • q ∨ r

   Hint

   Carefully swap the operators.

4. 4.

   True or False: The dual of a compound proposition is always logically equivalent to the original proposition.

   • True
   • False

   Hint

   Consider the definitions of dual and equivalence in logic.

5. 5.

   Construct the dual of the statement ((p ∧ (¬q)) ∨ r). Explain the significance of your result.

   Hint

   Focus on correctly applying the dual transformation rules.

6. 6.

   If P and Q are two logically equivalent statements, demonstrate how their duals maintain logical equivalence.

   Hint

   Refer back to the definitions of logical equivalence and apply transformations carefully.