Practice Satisfiability Of A Compound Proposition (7.3.1)

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6 sample questions

Question 1.
Rewrite the implication 'p → q' using conjunction and negation.
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Think about how implications can be transformed into disjunctions.
Question 2.
Is the proposition 'True OR False' satisfiable? Why?
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Remember, any disjunction is satisfied if at least one part is True.
3Question 3.
What does it mean for a proposition to be satisfiable?
- It is always false
- It can be made true with some assignments
- It is a tautology
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Think about the conditions that define satisfiability.
4Question 4.
True or False: A compound proposition can be satisfiable and a tautology at the same time.
- True
- False
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Reflect on the definitions of tautologies versus satisfiability.
Question 5.
Given the proposition '(p AND q) OR (NOT r)', find a truth assignment that satisfies it.
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Look to satisfy any part of the disjunction.
Question 6.
Formulate a proof showing that having just the negation operator can still create a valid logical expression.
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Think about how negation transforms the logical landscape.

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