Dr. A. Betten
Fall 2009
MATH 281 Introduction to Mathematical Reasoning
Assignment # 1
Problem # 1
Book, Exercise 1.1 page 8.
Problem # 2
Book, Exercise 1.4 page 8.
Problem # 3
Below are two sentences, one spoken in colloquial English, and the other in a mathematical
context. What does the sentence mean in the context in which it is spoken? Explain the
different usages of the word unique. Please write nice and clearly.
a) “At the Halloween party, everyone wore a unique hat!”
i) Everyone wore a hat, and no two people wore hats of the same style.
ii) Each person wore only one hat.
b) “For a function f : A → B, every element of A has a unique output in B.
i) Every x ∈ A has an output in B, and no two elements of A have outputs with the
same value.
ii) Each x ∈ A is sent to only one element of B.
Problem # 4
Is the following definition clearly stated and correct? Explain nice and clearly. Give a better
definition.
“Definition:” Given nonempty sets A and B, a function f : A → B is a rule that
assigns to each x ∈ A an element f (x) ∈ B. If f (x) is unique for every x ∈ A, then
f is said to be one-to-one.