7.5.2. Tautology Implication

Try these first

1. 1.

   Define functional completeness in your own words.

   Hint

   Consider how operators like AND, OR, and NOT interact.

2. 2.

   True or False: A tautology is always satisfiable.

   Hint

   Think about the definition of a tautology.

3. 3.

   Which of the following describes a tautology?

   • It is always false
   • It is always true
   • It depends on the context

   Hint

   Reflect on the nature of tautological statements.

4. 4.

   True or False: The statement 'p ∨ ¬p' is a tautology.

   • True
   • False

   Hint

   Think of both possible truth values for 'p'.

5. 5.

   Prove that conjunction and negation are functionally complete by expressing disjunction using only these operators.

   Hint

   Refer to De Morgan's laws for guidance.

6. 6.

   Construct a truth table for the expression '¬(p ∧ q)' and demonstrate that it is equivalent to 'p ∨ q'.

   Hint

   Break down the expression and assess each truth value.