Mathematics 55 Summer 2006
SolutionsProblem Set 4
3.4.6
Solution : The number of zeros at the end of 100! is just the number of times that 10 divides
100!. However, 10 is not prime, so it will not work just to take all the numbers between
1 and 100 that 1
Math 55 Discrete Mathematics
U.C. Berkeley Dept. of Mathematics
Summer 2007
Instructor Jared Weinstein
1075 Evans Hall
www.math.berkeley.edu/jared
[email protected]
Homework #1 Solutions
1.1.20 Write each of the following sentences in if . . . then
SOLUTION SET #3 FOR MATH 55
Note. Any typos or errors in this solution set should be reported to the GSI at [email protected] 2.4.10. What are the quotient and remainder when (a) 19 is divided by 7? (b) -111 is divided by 11? (c) 789 is divided by
SOLUTION SET 12DUE 5/7/2008
Problem 1 (#8.6.8). Determine whether the relations represented by the following
zero-one matrices are partial orders:
101
a) 1 1 0
001
100
b) 0 1 0
101
1010
0 1 1 0
c)
0 0 1 1
1101
Solution. By inspection, all three matrices
SOLUTION SET 11DUE 4/30/2008
Problem 1 (#8.4.2). Let R be the relation cfw_(a, b)|a = b on the set of integers.
What is the reexive closure of R?
Solution. Since R already includes all (a, b) for a = b, and we now must add the
(a, a), the reexive closure
SOLUTION SET 9DUE 4/16/2008
Problem 1 (#7.1.18). a) Find a recurrence relation for the number of permutations of a set with n elements.
b) Use this recurrence relation to nd the number of permutations of a set with
n elements using iteration.
Solution. Le
SOLUTION SET 8DUE 3/12/2008
This solution set is currently only partially complete, to allow a post before the
midterm.
Since I appear to have left my copy of the text in a locked oce in a locked
building 35 miles away, Ill write solutions from memory. Th
SOLUTION SET 7DUE 3/19/2008
Please report any errors in this document to Ian Sammis ([email protected]).
Problem 1 (#6.1.14). What is the probability that a ve-card poker hand contains
cards of ve dierent kinds?
Solution. The sample space here is
SOLUTION SET 6DUE 3/12/2008
This solution set is currently only partially complete, to allow a post before the
midterm. Please report any errors in this document to Ian Sammis ([email protected]).
Problem 1 (#5.3.12). How many bit strings of lengt
PARTIAL SOLUTION SET 4DUE 2/19/2008
In the interest of getting this out before the midterm, this is current a partial solution set only. Please report any errors in this document to Ian Sammis
([email protected]). For more practice try odd problem
SOLUTION SET 3DUE 2/13/2008
Please report any errors in this document to Ian Sammis ([email protected]).
Problem 1 (#3.1.4). Describe an algorithm that takes as input a list of n integers
and produces as output the largest dierence obtained by sub
SOLUTION SET 1DUE 1/30/2008
Please report any errors in this document to Ian Sammis ([email protected]).
Problem 1 (#1.1.8). Let p, q, and r be the propositions
p : You have the u.
q : You miss the nal examination.
r : You pass the course.
Express