COT3100.01, Fall 2002
Test #2
Print Name: ______________________________
S. Lang
(10/31/2002)
Social Security No.:
____________________
Instruction:
The test is a closed-book, closed-notes, and no-calculator test.
The test has 4 pages
(double-sided), 17 questions, and 100 total points.
The last sheet contains the relevant definitions,
principles, 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.
For combinatorics questions, you may
leave your
answers in an un-simplified form
, e.g.,
C
(10, 3), 5! / 3!, 2
9
* (2
4
+ 6 * 2
3
), etc. unless the question
says otherwise.
Your signature below indicates you have read and understood this instruction.
Signature: ______________________________________
Part I.
(39 pts., 3 pts. each) True/False, or short-answer, questions. (No explanation needed
and no partial credit given.)
1.
Let
N
denote the set of natural numbers {0, 1, 2, …}, and let