1. Find the midpoint of the interval with endpoints a = -10 and b = 16.

2. Find the second endpoint of the interval with one endpoint 3 and a midpoint -5.

3. Find the point that is 3/4 of the way from a to b if a = -6 and b = 14.

4. If 18 is midway between a and b and 12 is 3/10 of the way from a to b what is a and b?

5. If 2/7 of the way from a to b is 6 and 5/8 of the way from a to b is 25 what is a and b?

6. Let A = { -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8 }

a. Give { x | x Î A and -4 £ x < 2 }7. What is the set of letters in the state name MISSISSIPPI? What is the number of elements in that set?

b. Give { x | x Î A and 1 < x < -5 }

8. Define: the power set of a set A.

9. Give the power set of {a, b, c}

10. How many elements are there in the power set of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}? How many of these elements contains the number 6?

12. Let A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8, 10}

a. Find A Ç B.13. Let A = { 1, 2, 3, 4, 5, 6} and B = { {1, 2, 3}, {4,5,6} }

b. Find A È B.

c. Find A - B

d. Find B - A

a. How many elements are in A?14. If E = { 1,2,3,4,5,6} then

b. How many elements are in B?

c. What is A - B?

d. What is B - A?

a. is {2} Î E?15. Let A = { 1, 2, 3} and B = {3, 4}

b. is {2} Î 2^{E}? Why or why not?

a. Give 2^{A}- 2^{B}.

1. The components of a mathematical system.

a. What are primitive terms?2. Give truth tables for p ® q, p Ù q, ~p, and p ® ~q

b. What are axioms?

c. Give an example of an axiom.

d. Give the primitive terms in your example of an axiom.

e. What is the difference between a conjecture and a theorem?

3. Consider the following statement: If x is even then x2 is even.

a. Give the hypothesis of that statement.4. Let A = {1,2,3,4} and B={3,4,5,6}. Give a Venn diagram representing A and B. Within that Venn diagram indicate where the following values should go: 1,2,3,4,5,6,7, and 8.

b. Give the conclusion of that statement.

5. Direct proofs

a. Describe the concept of a direct proof.6. What is a syllogism?

b. Prove, using a direct proof: If x is divisible by 5 then x^{2}is divisible by 5.

7. The following pairs of logical forms are the premises of a syllogism. Give the conclusion of each syllogism.

a. If P then Q. If Q then R.8. Give the contrapositive of "If x

b. P. If P then R.