Practice Dual Of Compound Proposition (6.8.1) - Tutorial 1: Part I - Discrete Mathematics

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6 sample questions

Question 1.
What is the dual of 'P OR Q'?
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Recall the transformations for OR.
Question 2.
Is the proposition 'P' equal to its dual? Why or why not?
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Think about single literals.
3Question 3.
What is the dual of 'P AND Q'?
- P AND Q
- P OR Q
- TRUE
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Remember to switch the operations.
4Question 4.
If P is equivalent to Q, what can be said about their duals?
- True
- False
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Think of the relationship between duals.
Question 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?
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Apply the duality rules thoroughly.
Question 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?
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Think about the definitions of AND, OR, and their relations.

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