6.8.1. Dual of Compound Proposition

Try these first

1. 1.

   What is the dual of 'P OR Q'?

   Hint

   Recall the transformations for OR.

2. 2.

   Is the proposition 'P' equal to its dual? Why or why not?

   Hint

   Think about single literals.

3. 3.

   What is the dual of 'P AND Q'?

   • P AND Q
   • P OR Q
   • TRUE

   Hint

   Remember to switch the operations.

4. 4.

   If P is equivalent to Q, what can be said about their duals?

   • True
   • False

   Hint

   Think of the relationship between duals.

5. 5.

   Given propositions P, Q, and R, construct a dual of the compound proposition 'P AND (Q OR R)'. What does the resulting dual express?

   Hint

   Apply the duality rules thoroughly.

6. 6.

   Using the properties of duals, prove that if P AND Q is true, then the dual expression should also logically hold. What implications arise?

   Hint

   Think about the definitions of AND, OR, and their relations.