Practice Constructing Duals (6.8.2) - Tutorial 1: Part I - Discrete Mathematics

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6 sample questions

Question 1.
What is the dual of the proposition p ∧ q?
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Remember to switch ANDs with ORs.
Question 2.
Construct the dual for p ∨ q.
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Think about the dual transformation.
3Question 3.
What is the dual of the expression p ∧ (q ∨ r)?
- p ∨ (q ∧ r)
- p ∧ r
- q ∨ r
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Carefully swap the operators.
4Question 4.
True or False: The dual of a compound proposition is always logically equivalent to the original proposition.
- True
- False
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Consider the definitions of dual and equivalence in logic.
Question 5.
Construct the dual of the statement ((p ∧ (¬q)) ∨ r). Explain the significance of your result.
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Focus on correctly applying the dual transformation rules.
Question 6.
If P and Q are two logically equivalent statements, demonstrate how their duals maintain logical equivalence.
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Refer back to the definitions of logical equivalence and apply transformations carefully.

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