2.5.1. Using Logical Identities for Simplification

Try these first

1. 1.

   What is a tautology? Provide an example.

   Hint

   Think of a statement that can't be false.

2. 2.

   What happens when you negate 'p and q'?

   Hint

   Consider how negation distributes.

3. 3.

   What is the statement 'p or not p' classified as?

   • Contradiction
   • Tautology
   • Contingency

   Hint

   It cannot be false under any condition.

4. 4.

   True or False: The contrapositive of 'If p then q' is 'If q then p'.

   • True
   • False

   Hint

   Remember the definitions clearly.

5. 5.

   Prove that the expressions 'not (p and q)' and 'not p or not q' are equivalent using truth tables.

   Hint

   Make sure to list all combinations for p and q.

6. 6.

   Using logical identities, simplify the expression 'not (p or (q and r))' step-by-step.

   Hint

   Work through transformation phases slowly.