CS 30
Fall 2014
Discrete Mathematics
1. Dene
=
Homework 4 Solutions
Amit C, Suman B, Sagar K, Zhao T
Computer Science Department
Dartmouth College
cfw_0. Let n, k .
1.1. Let Sn,k be the possible nonnegative integer solutions to the inequality x 1 + x 2 +

CS 30
Fall 2014
Discrete Mathematics
Homework 7 Solutions
Amit C, Suman B, Sagar K, Zhao T
Computer Science Department
Dartmouth College
1. Solve Problem 19.11 (all parts) from the [LLM] book.
Solution
(a) We claim that
[R] can be any large. Consider a tw

CS 30
Fall 2014
Discrete Mathematics
Homework 5 Solutions
Amit C, Suman B, Sagar K, Zhao T
Computer Science Department
Dartmouth College
1. Solve Problem 16.2, parts (a) and (b), from the [LLM] book.
16.2 Part (a): Each of the k digits is picked from 10 d

CS 30
Fall 2014
Discrete Mathematics
Amit C, Suman B, Sagar K, Zhao T
Computer Science Department
Dartmouth College
Homework 2 Solutions
Throughout this homework, refers to the set of all integers, refers to the set of all natural numbers
(i.e., positive

CS 30
Fall 2014
Discrete Mathematics
Amit C, Suman B, Sagar K, Zhao T
Computer Science Department
Dartmouth College
Homework 6 Solutions
1. Alice and Bob are taking an advanced Computer Science course. The course has only three
grades: A, B, and C. The pr

CS 30
Fall 2014
Discrete Mathematics
Homework 3 Solutions
Amit C, Suman B, Sagar K, Zhao T
Computer Science Department
Dartmouth College
The general guidelines and submission instructions are the same as for Homework 1.
Throughout this homework,
refers to

CS 30
Fall 2014
Discrete Mathematics
Throughout this homework,
Homework 1 Solutions
Amit C, Suman B, Sagar K, Zhao T
Computer Science Department
Dartmouth College
refers to the set of all integers.
1. (Roster and Set-Builder Notations) Here are some sets

CS 30
Fall 2014
Discrete Mathematics
Homework 7 Solutions
Amit C, Suman B, Sagar K, Zhao T
Computer Science Department
Dartmouth College
1. Solve Problem 19.11 (all parts) from the [LLM] book.
Solution
(a) We claim that
[R] can be any large. Consider a tw

CS 30
Fall 2014
Discrete Mathematics
Homework 8 Solutions
Amit C, Suman B, Sagar K, Zhao T
Computer Science Department
Dartmouth College
1. Prove the nal step in the Tree Theorem: that (6) = (1). Refer to the lecture notes on the website.
Solution: We pro