MATH-UA.120: Discrete Mathematics
Practice Midterm Exam I
Fall 2016
(1) (12 points; 3 points each) For each of the following statements, determine whether it
is True (write T) or False (write F). No proofs or counterexamples required.
(a) Any relation whi

Notes on proof by Well-Ordering Principle
Oct 13, 2016
The textbook discusses the method of proof by smallest counterexample, or equivalently proof by WellOrdering Principle. The scheme goes as follows:
1. Begin with a statement P for natural numbers x.
2

Discrete Math, Homework 2
Due Sep 20, 2016
1 (8 points). For all a, b Z, prove that
cfw_x Z : x|a cfw_x Z : x|b
if and only if
a|b.
2 (4 points each; 2 points each subproblem) Complete the following exercises from the textbook:
8.11, 8.15, 8.18, 9.15(a)(d

Discrete Math Midterm Exam
Name:
Time: 9am-10:40am, 10/23/2014
Problem
1
2
3
4
5
6
7
Total
Points
Problem 1 (10 points)
How many integers between 1 and 200 (including 1 and 200) are divisible by 2 or 3
(including the integers divisible by 2 and 3)? Write

5. Product, Quotient, and Chain Rules; Implicit Differentiation
1. Compute derivatives for the following functions. You do not need to fully simplify your answers to (c) and (d).
(a) x1 (x2 + 1) x
x+1
(b)
x1
x2
(c)
x+1
(x + 1)(x 1)
(d)
(x2 + 2)(x + 3)
So

Discrete Math Final Exam
Name:
Time: 8am-9:50am, 12/16/2014
Problem
1
2
3
4
5
6
7
Total
Points
Problem 1 (20 points)
Toss a fair coin for 5 times.
(1) Let A be the event there are no two consecutive tails, and B be the event that
the first result is a tai

Math for Econ I- Practice Problems
New York University
1. Supply and demand
1. In a California town, the monthly charge for waste collection is $8 for 32 gallons of waste and $12.32 for 68 gallons
of waste.
(a) Find a linear formula for the cost, C, of wa

MATH 120.001 - DISCRETE MATHEMATICS
Workshop 8
Discuss workshop problems in small groups of 3-4 students. It will be helpful to discuss all problems in
this set during class time and save the details of each problem for your write-up. Your write-up should

Discrete Math Midterm Exam
Name:
Time: 9am-10:40am, 10/23/2014
Problem
1
2
3
4
5
6
7
Total
Points
Problem 1 (10 points)
How many integers between 1 and 200 (including 1 and 200) are divisible by 2 or 3
(including the integers divisible by 2 and 3)? Write

Discrete Math Midterm Exam
Name:
Time: 9am-10:40am, 10/23/2014
Problem
1
2
3
4
5
6
7
Total
Points
Problem 1 (10 points)
How many integers between 1 and 200 (including 1 and 200) are divisible by 2 or 3
(including the integers divisible by 2 and 3)? Write

Discrete Math Midterm Exam
Name:
Time: 9am-10:40am, 3/12/2015
Problem
1
2
3
4
5
6
7
Total
Points
Problem 1 (20 points)
Let A = cfw_1, 2, 3 and B = cfw_3, 4, 5, and C = 2A .
(1) Write down A B, A B, A B, AB, A B.
Solution.
AB
AB
AB
AB
AB
= cfw_1, 2, 3, 4,