# CMPSCI 250: Introduction to Computation

### David Mix Barrington

### Fall, 2007

# Homework Assignment #7

#### Posted Tuesday 27 November 2007

#### Due on paper in class, Friday 14 December 2007

There are eleven questions for 100 total points plus 10 points extra credit.
All are from
the textbook, *A
Mathematical Foundation for Computer Science*, the third (purple) course
packet. "Problem 1.1.2", for
example, is at the end of Section 1.1 and is labeled "P1.1.2".
The number after each problem is its individual point value. Make sure
you don't do an Exercise when a Problem is assigned! (Though the Exercises
should be good practice and the answers to them are in the back of the book
for Chapter 6, at least.)

Students are responsible for understanding and following
the academic honesty
policies indicated on this page.

All the questions in this assignment are **group**
questions -- please hand on one paper per group. The groups are the
same as those for HW#5 -- please email me with any questions or concerns.

- Pages 6-14 and 6-15: Problem 6.2.5 (10)
- Pages 6-18 and 6-19: Problem 6.3.2 (10)
- Pages 6-23 and 6-24: Problems 6.4.7 parts a,b, and c (10), 6.4.7 part
d (10 XC). Please note the corrections on this problem and a different hint:
"You may find it easier to prove the formula S(n,k) = k(S(n-1,k) + S(n-1,k-1))
and then use this formula to prove a formula for S(n,n-1) by induction. To
prove the formula, first count the functions f from A to B where f(1) is needed
to make f onto, then count the functions where it is not."
- Pages 6-33 and 6-34: Problem 6.6.3 (10)
- Pages 6-38 and 6-39: Problems 6.7.2 (10), 6.7.4 part a (10), and 6.7.4 part
b (10).
- Pages P-5 and P-6: Problems P.1.3 (10) and P.1.4 (10)
- Pages P-13 and P-14: Problem P.2.5 part c (10)

Last modified 27 November 2007