I. (10 pts.) Using only terms that appear in the first chapter (in the chapter or in exercises we have been assigned), define parallelogram. Recall from plane geometry that a parallelogram is a quadrilateral (a figure with four distinct sides, intersecting only at the endpoints of the sides) with opposite sides parallel.

2. (10 pts.) Define the two terms interpretation and model.

3. (20 pts.) Consider the statement

"If it rains today, I will stay home"

a. What is the converse of the statement? (re-write as a

normal statement in English)

b. What is the contrapositive of the statement? (re-write as a

normal statement in English)

c. What is the sufficient condition in this statement?

d. What is the necessary condition in this statement?

4. (15 pts.) Negate the following three statements, writing the negation in ordinary English.

a. If I jump in the water, I get soaked.

b. All birds fly.

c. If P and Q are distinct points, then there is a unique line

incident to both.

5. (10 pts.) Logic rule 5 says that "" means the same as "". Use this and other logic rules to demonstrate that "" means the same as "". Show the steps in your reasoning. Hint: Try replacing with and with . This is the other DeMorgan law.

6. (10 pts.) Demonstrate that if l1 and l2 are two distinct intersecting lines, then they intersect in exactly one line.

7. (5 pts.) Consider the statement "Lines are infinite in length". We can't give a proof of this just yet, but how might you justify such a statement using the axioms we have seen so far?

8. (10 pts.) Justify the statement "The parallel postulate is independent of the incidence axioms".

9. (10 pts.) What is the reason for studying this? More explicitly, what are some of the advantages of the axiomatic method?