MATH 120 Practice Problems
Learning Objective 1.4
The following exercises are to help you practice the concepts for Learning Objective 1.4.
You are encouraged to work with other students on these exercises.
If you have any questions, post them in our class discussion board.
Questions from Section 0.3 of Discrete Mathematics: An Open Introduction
uestions 10, 14, and 16
Additional Discussion Questions
1. Let W be the set of binary words of length 9. Let X be the set of binary words of length 9
that start with the digits q Let Y be the set of binary words of length 9 that end with
the digits 00Š(a) Is X ? W ? Is Y ? W ?
(b) Are X and Y disjoint?
(c) Describe X ? Y in words.
(d) Describe (X ? Y )c in words using the word Ò)nstead of NDŠ(e) Is the Ò9ou used in part (d) an inclusive OR or an exclusive OR?
2. Translate the sentence
Every outfit I wear either has black shoes or brown socks, but not both.
into mathematical notation and draw a Venn Diagram to visualize what it means.
3. Use De MorganàLaws to describe the following sets in words.
(a) There are people at Queens College who are taking classes in both Kiely Hall and in
Queens Hall. Describe the people at Queens College not in this set.
(b) There are families with pets who have dogs or have cats or have birds. Describe the
families with pets that are not in this set.
4. What is the opposite of the statement ¯r my birthday I will receive an elephant or a
hippopotamus, but not both?µ. De MorganàLaws can be extended to more sets.
(a) Show that (A ? B ? C)c = Ac ? B c ? C c using Venn Diagrams
(b) Show that (A ? B ? C)c = Ac ? B c ? C c using Venn Diagrams
6. Is the power set of {2, 3, 4, 5} a subset of the power set of {1, 2, 3, 4, 5, 6}? Why or why not?
7. Partition the set {a, b, c, d} into two non-empty disjoint sets in all possible ways.

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