Math 110 Review for Exam-1 Spring 2002
1. Construct a Venn diagram to determine the validity of the given argument.
1. No professor is a millionaire.
2. No millionaire is illiterate.
Therefore, no professor is illiterate.
2. Construct a Venn diagram to determine the validity of the given argument.
1. Real men don’t eat quiche.
2. Real men go hunting.
Therefore, hunters don’t eat quiche.
3. Construct a truth table to determine whether the two statements are equivalent.
If you work hard, you will succeed.
You will not succeed or work hard.
4. Construct a truth table to determine whether the two statements are equivalent.
She is a member of a sorority or she is a foreign student.
If she is not a member of a sorority, then she is a foreign student.
5. Construct a truth table for the following expression: (p∧r)→∼ (q∨ ∼ r).
6. Copy the Venn diagram on the right and shade the region corresponding to the indicated
set. (a) A∩B0. (b) (A∪B)0. (c) A0∪B. (c) (A∪B)0.
7. Let Sdenote the set {Spring , Summer, F all, W inter}.
(a) List all subsets with exactly three elements.
(b) How many subsets with exactly two elements are there? (It is not necessary to list them.)
(c) If A={F all, W inter }, find all subsets of A.
8. Write a sentence that represents the negation of the statement:
No student likes the instructor.
9. In a recent socioeconomic survey, 600 married women were asked to check the appropri-
ate circle or circles on the following form:
I have a career. I have a child.
The results were as follows: 411 checked the child circle. 125 checked the child circle and the
career circle, and 139 were blank (no circles checked). Find the following:
(a) The number of participating women that checked only the child circle.
(b) The number of participating women that checked only the career circle.
10. License plates for the city of Mobile have the following form:
2A . The first two blanks are letters and the last three blanks are digits. How many
different license plates are possible given the following conditions?
(a) Letters and digits can be repeated.
(b) Letters and digits cannot be repeated.
(c) The letters cannot be repeated but the digits can be repeated.
11. A personal identification number or PIN is a four-digit number that allows repetition
of digits.
(a) How many PIN’s are possible?
(b) How many of these numbers contain no repeated digits?
(c) What is the percentage of PIN’s that have at least one repeated digit?
Additional Problems:
Section 1.1,Problems 5, 7, 15, 17
Section 1.2,Problems 5, 7, 19
Section 1.3,Problems 13, 17, 27, 31, 35, 43
Section 2.1,Problems 9, 17, 21, 23, 25, 27, 29, 30, 35, 52
Section 2.3,Problems 7, 11, 16, 17, 21