1. Using logic simplification determine if the following proposition is a tautology. Show all the steps. DO NOT USE TRUTH TABLE.

((p q) p ) q

2. Using logic simplification determine if the following proposition is a contradiction. Show all the steps. DO NOT USE TRUTH TABLE.

p (pq) q

3. Prove that p q (p q) (pq).

Hint. Obtain a logic expression of the left hand term taking the TRUE logic from its truth table. Then simplify the expression.

If M: p q and N: q p, can you say if MN will be a tautology? Why or why not? Justify your answer.

4. "If there is a printer (p) that is either out of service or busy, then some job (j) is lost" - identify the predicates and logical expression for this statement.

Identify a logical expressions for the following statement, "Every student in the class knows either JAVA or C++."