Class Notes: Applied Discrete Structures
Spring Semester 1999 - MWF 5th Period CSE/E222, Section 4617X
Quiz #1 -- Solution
Question 1. (5 points) Given nonempty sets A, B, and C, prove or
disprove the following statement:
(A 
B)
(A C)
ø .
Solution. From the distributive property, (A
B)
(A C) =
A (B
C).
Two cases pertain:
Case 1. If B and C are disjoint, then
B C =
ø , and
A ø
= A.
Case 2. If B and C are conjoint, then
B C
ø ,
and A (B
C)
ø .
Conclusion. Hence, the statement
(A B)
(A C)
ø is true.
Question 2. (5 points) Is a function an injection, a
surjection, or a bijection?
Solution. This is a tricky question, which can be answered
from your textbook (pp. 59-60). Namely, a function is injective
if it is one-to-one. A function is called a surjection
if it is onto. Finally, a function is a bijection if
it is both one-to-one and onto.
Copyright © 1999 by Mark S. Schmalz.