Practice Question 13 (7.7) - Tutorial 1: Part II - Discrete Mathematics

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6 sample questions

Question 1.
What is the definition of a clause?
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Consider the component parts of a logical statement.
Question 2.
Identify a pair of complementary literals.
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Think about variables and their negations.
3Question 3.
What does the resolution method help determine?
- Satisfiability of a single clause
- Whether a compound proposition is true
- Satisfiability of a set of clauses
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Think about the purpose of adding multiple clauses.
4Question 4.
True or False: A set of clauses is unsatisfiable if they cannot all be true at the same time.
- True
- False
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Envision cases where truth values lead to contradictions.
Question 5.
Prove unsatisfiability of the compound proposition formed by the clauses: { (p ∨ q), (¬p), (¬q) } using resolution.
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Start with deriving conclusions iteratively.
Question 6.
Given the clauses: { (p ∨ r), (¬r ∨ q), (¬q ∨ ¬p) }, show how they lead to unsatisfiability.
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Be consistent with tracking the literals.

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