COT3100.01, Fall 2002
Final Exam (Test #3)
Print Name: ____________________________
S. Lang
(12/03/2002)
Social Security No.:
__________________
Instruction:
The test is a closedbook, closednotes, and nocalculator test.
The test has 6 pages
(doublesided), 11 questions, and 100 total points.
The last two sheets (3 pages) contain the
relevant definitions, formulas, and theorems from the notes, which you can tear off and use for
reference.
In writing your proofs, you need to show all the steps, and explain each by using the
appropriate definition or theorem, by either stating the name, stating the actual contents, or giving
its reference number as shown on the reference sheet.
Your signature below indicates you have
read and understood this instruction.
Signature: ______________________________________
Part I.
(36 pts., 3 pts. each) True/False, or shortanswer, questions. (No explanation needed
and no partial credit given.)
1.
Let
A
= {1, 2, 3, 4} and let
R
⊆
A
×
A
denote a binary relation depicted by the directed graph
given in the figure.
Answer each of the following True/False questions:
2.
Define two realvalued functions
f
: [0,
∞
)
→
R
and
g
:
R
→
R
by the following formulas, where
the set [0,
∞
) denotes the set of nonnegative real numbers, and
R
denotes the set of all real
numbers,
f
(
x
) =
x

1, and
g
(
x
) = 2
x
+ 1.
Answer the following questions: