McGill University
Faculty of Science
Solutions to Practice Final Examination
Math 240
Discrete Structures 1
Time: 3 hours
Marked out of 60
Question 1.
[6]
Prove that the statement (p q ) (q r) (p r) is a contradiction
using truth tables or the rules of lo
Monday 10th December
Math 240: Discrete Structures I
Final Exam
Instructions. The exam is 3 hours long and contains 6 questions. Write your
answers clearly in the notebo ok provided. You may quote any result/theorem
seen in the lectures or in the assignme
Math 240
Solutions to Assignment 2
[email protected]
Question 1.
(a) (b) Prove that for positive integers k and n with k n, Find the numerical value of 10000 / 9999 . 5000 4999
n k
[4] =
n nk
.
Solution 1.
(a) By denition they are equal since n k = n! n
CLASS NOTES MATH 240
Notes on Logic
1
Propositional Calculus
A proposition or statement is an assertion which can be determined to be
either true or false (T or F). For example, zero is less than any positive
number is a statement. We are interested in co
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Tuesday 11 October 2016.
Hand in to the mailbox at Burnside 1005.
Homework assignment 2: Predicate Logic,
Set Identities
Discussing the assignment with other students is allowed (and
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Thursday 29 September 2016.
Hand in to the mailbox at Burnside 1005.
Homework assignment 1: Propositional Logic
Discussing the assignment with other students is allowed (and encourage
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Monday 7 November 2016.
Hand in to the mailbox at Burnside 1005.
Homework assignment 4: Congruences,
Functions
Discussing the assignment with other students is allowed (and encouraged
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Friday 21 October 2016.
Hand in to the mailbox at Burnside 1005.
Homework assignment 3: Mathematical
induction and number theory
Discussing the assignment with other students is allow
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Monday 21 November 2016.
Hand in to the mailbox at Burnside 1005.
Homework assignment 6: Combinatorics and
graph theory
Discussing the assignment with other students is allowed (and e
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Thursday 29 September 2016.
Hand in to the mailbox at Burnside 1005.
Solutions to homework assignment 1:
Propositional Logic
Discussing the assignment with other students is allowed (
Math 240: Discrete Structures I
Practice Midterm
Instructions. The exam is 50 minutes long and contains 2 questions. You may
quote any result/theorem seen in the lectures or in the assignments without proving
it (unless, of course, it is what the question
Math 240: Discrete Structures I
Practice Exam A - Solutions
1. Logic.
(a) The negation is
n N (n3 + 6n + 5 is odd n is odd)
(b) If n is odd then n3 + 6n + 5 is even because n3 is then odd and 6n is then
even. So the original statement is true.
(c) The tru
Math 240: Discrete Structures I
Assignment 6: Sketch Solutions
1. Cycles and Circuits.
(a) A graph on 11 vertices contains at most 11 = 55 edges. So G is a
2
complete graph on 11 vertices minus two edges. These two edges may or
may not share an endpoint.
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Monday 14 November 2016.
Hand in to the mailbox at Burnside 1005.
Homework assignment 5: Combinatorics and
counting
Discussing the assignment with other students is allowed (and encou
MATH 240: Discrete Structures I (Winter 2017)
Times: Monday-Wednesday-Friday: 11:35 - 12:35, MAAS 112.
Instructor: Bruce Shepherd (Office: Burnside 1113, Email: [email protected])
Office Hours: Tuesday 3:00-4:30. And also by appointment.
Webpage: w
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Monday 21 November 2016.
Hand in to the mailbox at Burnside 1005.
Homework assignment 6: Combinatorics and
graph theory
Discussing the assignment with other students is allowed (and e
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Friday 21 October 2016.
Hand in to the mailbox at Burnside 1005.
Homework assignment 3: Solutions
Discussing the assignment with other students is allowed (and encouraged!) but you
sh
Math 240: Discrete Structures I
McGill University, Fall 2016, 24 October
Midterm exam
The exam is 50 minutes long and contains two multi-part questions. All parts are equally
weighted. Write your answers clearly in the notebook provided. You may quote any
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Tuesday 11 October 2016.
Hand in to the mailbox at Burnside 1005.
Homework assignment 2: Solutions
Discussing the assignment with other students is allowed (and encouraged!) but you
s
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Tuesday 11 October 2016.
Hand in to the mailbox at Burnside 1005.
Homework assignment 2: Predicate Logic,
Set Identities
Discussing the assignment with other students is allowed (and
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Monday 21 November 2016.
Hand in to the mailbox at Burnside 1005.
Homework assignment 6: Combinatorics and
graph theory
Discussing the assignment with other students is allowed (and e
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Monday 14 November 2016.
Hand in to the mailbox at Burnside 1005.
Homework assignment 5: Combinatorics and
counting
Discussing the assignment with other students is allowed (and encou
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Monday 7 November 2016.
Hand in to the mailbox at Burnside 1005.
Solutions to Homework assignment 4:
Congruences, Functions
Discussing the assignment with other students is allowed (a
Math 240: Discrete Structures I
McGill University, Fall 2016
Due 4:30pm Friday 21 October 2016.
Hand in to the mailbox at Burnside 1005.
Homework assignment 3: Solutions
Discussing the assignment with other students is allowed (and encouraged!) but you
sh
Course outline Math 240: Discrete Structures I
Instructor information
Name: Dr. Evan DeCorte
E-mail: [email protected]
Office hours: Friday 11:30-12:30 in 1120 Burnside, or by appointment
Course URL: www.math.mcgill.ca/~edecorte/math240/
TA information