2.3.3. Distributive Law

Try these first

1. 1.

   Define logical equivalence.

   Hint

   Think about the truth values they represent.

2. 2.

   What is a tautology?

   Hint

   Recall examples like 'p or not p'.

3. 3.

   What does the Distributive Law state?

   • A. p and (q or r) = (p and q) or (p and r)
   • B. p or (q and r) = (p or q) and (p or r)
   • C. Neither A nor B

   Hint

   Consider how conjunction behaves with operators.

4. 4.

   Is (p and -p) a contradiction?

   • True
   • False

   Hint

   Remember the definition of contradiction.

5. 5.

   Demonstrate the steps to prove that p and (q or r) simplifies logically to (p and q) or (p and r) using truth tables, and explain each step.

   Hint

   Detailed tracking of truth values is key.

6. 6.

   Given the expression p or (q and r), transform and prove it equivalent to (p or q) and (p or r) using the Distributive Law.

   Hint

   Breaking down each piece helps in clarity.