7.6.1. Using Resolution for Validity

Try these first

1. 1.

   What does it mean for a set of operators to be functionally complete?

   Hint

   Think about combining basic logical statements.

2. 2.

   Convert the implication 'p → q' using logical operators.

   Hint

   One operator should represent FALSE.

3. 3.

   What are the main logical operators in a functionally complete set?

   • Conjunction
   • Negation
   • Disjunction
   • Only Disjunction
   • Only Conjunction

   Hint

   Recall the operators discussed.

4. 4.

   T or F: A tautology is a proposition that is always false.

   • True
   • False

   Hint

   Think about the definition of tautology.

5. 5.

   Using the premises 'p → q', 'q → r', and '¬p', show whether the conclusion '¬r' is valid using resolution.

   Hint

   Start with negating the conclusion!

6. 6.

   You are given a chain of implications, can you derive a numeric example using resolution that leads to either a tautology or contradiction?

   Hint

   Think about testing minimal values to break the chain.