7.8.1. Verification of Valid Argument

Try these first

1. 1.

   Define what functionally complete means.

   Hint

   Think about which logical operations are necessary to represent all truths.

2. 2.

   What is the negation of 'p AND q'?

   Hint

   Use De Morgan's Law to find this.

3. 3.

   What is a functionally complete set of logical operators?

   • A set of operators that can express all propositions
   • A set that only consists of negation
   • Any random set of operators

   Hint

   Consider the ability to represent various logical outcomes.

4. 4.

   Is the statement 'p AND q → r' a valid argument?

   • True
   • False

   Hint

   Think about what you need to ensure a conclusion is valid.

5. 5.

   Prove using resolution that the argument 'p ∨ q, ¬q ⟹ p' is valid.

   Hint

   Sketch out the resolution tree to visualize.

6. 6.

   Construct a truth table for the statement 'p → (q ∧ r)' and determine its validity.

   Hint

   Remember, a true conclusion arises from all true premises.