1. Give the inverse, converse and contrapositive for the following statement:
If the patient takes the medication, then he will have some side effects.
2. Calculate. Let A = {1, 2, 3}, B = {4, 5, 6}, C = {1, a, b, c}
a. A ? C =
b. A ? B =
c. A - C =
3. Relations and Functions:
a. Does the following arrow diagram illustrate a function f:XàY? Tell why or why not.
b. Represent the arrow diagram above as a set of ordered pairs.
4. Evaluate the following logical expressions with and .
5. Draw the arrow diagram and the matrix representation for the following relation on the set {1, 2, 3, 4}: R = { (1, 1), (2,2), (4, 3), (3, 2), (2, 1), (1, 3), (4,2), (2,3) }.
6. Find the first four terms of the recursively defined sequence , for all integers , where .
7. Div and Mod
a. Does 11 | 121? Explain why or why not.
b. What is 278 mod 12? Explain why your answer is correct.
8. A PIN can be either 2 or 3 characters long. How many PINs can you make from the digits 0 - 9 without repetition of digits?
9. If you roll two standard six-sided dice and take the sum of the numbers on each die, which sum happens most often? Be sure to show your work for full credit.
10. Use the diagram below to answer the questions.
Which vertices are the ancestors of vertex f?
Which vertices are the descendants of vertex f?
List the leaves in the tree.
What is the height of the tree?
List the level 3 vertices.