7.1.1. Lecture - 07

Try these first

1. 1.

   List the three functionally complete logical operators.

   Hint

   Think about basic operations in logic.

2. 2.

   What is the negation of p ∧ q?

   Hint

   Apply De Morgan's law.

3. 3.

   Which of the following sets of operators is functionally complete?

   • {AND
   • NOT}
   • {OR
   • NOT}
   • {AND
   • OR
   • NOT}

   Hint

   Think of basic operations in logic.

4. 4.

   True or False: p → q is equivalent to ¬p ∨ q.

   • True
   • False

   Hint

   Recall definition of implication.

5. 5.

   Demonstrate the validity of the argument where A, A → B, and B → C lead to C using resolution.

   Hint

   Apply the resolution method stepwise, canceling variables.

6. 6.

   You are given ¬(p ∨ q). Show its implications using resolution.

   Hint

   De Morgan’s laws will be helpful for transformations.