Practice Proving Functionality With Three Operators (7.2.2)

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6 sample questions

Question 1.
What does it mean for a set of operators to be functionally complete?
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Think about what types of statements can be created.
Question 2.
Rewrite the implication p → q using conjunction and negation.
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Remember how we can break down implications.
3Question 3.
What is the definition of a functionally complete set?
- A set that cannot express all propositions
- A set that can express all possible propositions
- A set of three operators only
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Think about the utility of the operators.
4Question 4.
Is the statement p → q equivalent to ¬p ∨ q?
- True
- False
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Relate this to the definitions you've learned.
Question 5.
Using only the operators AND and NOT, prove how you can express the complex proposition p || (q && r).
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Question 6.
Show that a biconditional can be transformed into disjunctions and negations and then back into its original form, demonstrating the reversibility of logical identities.
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