Assignment 4 Solutions
Problem1: (Section 2.1 Exercise 9) (a.) List all the subsets of the set cfw_a, b, c, d which
contain:
(i.) four elements
(ii.) three elements
(iii.) two elements
(iv.) one element
(v.) no elements
Solution:
(i.) cfw_a, b, c, d
(ii.)
MATH 2320
Test 2
Name:
Student Id:
There are eight problems (check that you have 10 pages). You have 50 minutes to write
the solutions. Solutions are expected to be short. In the case of proofs, one or two short
paragraphs should be the average length. Wr
PMAT 2320 Discrete Mathematics
Sample Midterm Test with Solutions
Problem #1
Write down the converse, the contrapositive and the negation of each of
the following implications:
(a) If a and b are integers, then ab is an integer.
(b) If x2 + x 2 < 0 then x
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Assignment 2
Mathematics 2320
Winter 2014
Due: January 31, 2014. SHOW ALL WORK
1. For each statement, (i) represent it as a formula, (ii) find the negation (in simplest form)
of
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Assignment 2 Mathematics 2320 Winter 2014
Due: January 31, 2014. SHOW ALL WORK
1. For each statement, represent it as a formula, (ii) ﬁnd the negation (in Simplest form)
of this
2.
3.
4.
5.
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Assignment 1 Mathematics 2320 Fall 2014
Due: January 24 , 2014 . SHOW ALL WORK
Suppose that the statements 1), q, 7‘, and s are assigned the truth values T, F, F, and
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Assignment 1 Mathematics 2320 Fall 2014
Due: January 24 , 2014 . SHOW ALL WORK
1. Suppose that the statements 1), q, r, and s are assigned the truth values T, F, F, and
T, re
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Assignment 3
Mathematics 2320
Winter 2014
Due: February 7 , 2014 . SHOW ALL WORK
1. List all the elements of the set A = cfw_x Z| |4x 1| < 15
2. Give an example of a set A such t
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Assignment 3 Mathematics 2320 Winter 2014
Due: February 7 , 2014 . SHOW ALL WORK
1. List all the elements of the set A = {m 6 Z| I42: - 1| < 15}
2. Give an example of a set A suc
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Assignment 4
Mathematics 2320
Winter 2014
Due: February 21 , 2014 . SHOW ALL WORK
1. Prove each of the following:
(a) A (B C) = (A B) (A C)
(b) Prove that if A, B, C, and D are a
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Assignment 5 Mathematics 2320 Winter 2014
Due: February 28 , 2014 . SHOW ALL WORK
1. Determine whether each of the following relations is a partial order and state whether
ea
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Assignment 5 Mathematics 2320 Winter 2014
Due: February 28 , 2014 . SHOW ALL WORK
1. Determine whether each of the following relations is a partial order and state whether
ea
l.
4.
10.
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Assignment 4 Mathematics 2320 Winter 2014
Due: February 21 , 2014 . SHOW ALL WORK
Prove each of the following:
(a) Ax(BUC)=(AxB)U(A><C) .
(b) Prove that if A, B, C', an
MATH 2320
Test 1
Name:
Student Id:
There are seven problems (check that you have 8 pages). You have 50 minutes to write
the solutions. Solutions are expected to be short. In the case of proofs, one or two short
paragraphs should be the average length. Wri
MATH 2320
Test 2
Name:
Student Id:
There are eight problems (check that you have 10 pages). You have 50 minutes to write
the solutions. Solutions are expected to be short. In the case of proofs, one or two short
paragraphs should be the average length. Wr
Midterm Exam
MATHEMATICS 2320
Fall 2004
Unless stated to the contrary, every answer should be justied using good clear English.
Time: 50 minutes
[6]
1. Write down the converse, the negation and the contrapositive of
If p(x) is a polynomial of odd degree,
Assignment 5:
Problem 1: (Section 2.5 Exercise 1) Determine whether or not each of the following
relations is a partial order and state whether or not each partial order is a total order.
(d.)(N N, ), where (a, b)
(e.) (N N, ), where (a, b)
(c, d) if and
M2320-Assignment 6: Solutions
Problem 1: (Section 6.1 Exercise 14) How many integers between 1 and 1000 (exclusive)
are not divisible by 2, 3, 5, or 7?
Solution:
(a.)
Let A, B , C , and D be the sets of integers between 1 and 1000(inclusive) which are
div
Math-2320 Assignment 7 Solutions
Problem 1: (Section 7.1 Exercise 4) There are 30 people in a class learning about permutations. One after another, eight people gradually slip out the back door. In how many
ways can this exodus occur?
Solution:
There are
Assignment 3 Solutions
Problem1: (Section 1.2 Exercise 8) Consider the following assertions.
A:There exists a real number y such that y > x for every real number x
B:For every real number x, there exists a real number y such that y > x
Solution:
A: False.
Assignment 2 Solutions
Problem 1: (Section 1.4 Question 2) Simplify each of the following statements.
(c.)[(p q ) (q r)] (r s)
Solution:
(c.)
[(p q ) (q r)] (r s)
[p q q r] (r s)
[(p r) (q q )] (r s)]
[(p r) 1] (r s)
1 (r s)
r s
r s
The above is de
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Answers for Sample Final exam Mathematics 2320
April, 2005
Instructor Margo Kondratieva
1. Find converse, contrapositive and negation of statement:
If it snows tonight, I will st
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Sample Final exam Mathematics 2320
April, 2005
Instructor Margo Kondratieva
1. Find converse, contrapositive and negation of statement:
If it snows tonight, I will stay at home.
Assignment1 Solutions
Problem 1:Classify each of the following statements as true or false and explain your
answers.
(b.)4 = 2 + 2 and < 50
7
(d.)4 = 2 + 2 7 < 50
(f.)4 = 2 + 2 7 < 50
(h.) The area of a circle of radius r is 2r or its circumference is r2
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
The necessary condition for Final exam Mathematics 2320
April, 2005
Instructor Margo Kondratieva
The necessary condition 1 to pass the Final Exam is to know denitions of the foll
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Mathematics 2320
Final Exam
Winter 2000
Marks
[22]
1. (a) How many elements are in the power set of cfw_a, b?
(b) State the range of the function g : Z Z dened by g(x) = |x| + 3.
Midterm Exam
MATHEMATICS 2320
Winter 2002
It is expected that all answers will be justied.
1. Let A be the implication
A: If a, b, u, v are integers and au + bv = 0, then a = b = 0.
[9]
(a) Write down the converse, the negation and the contrapositive of A
Midterm Exam
MATHEMATICS 2320
October 1997
1. Consider the statement
A: Every odd integer is divisible by 3 or 5.
[2]
(a) Express A as an implication. Is A true? Proof or counterexample.
[2]
(b) What is the converse of A? Is this converse true? Proof or c
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Assignment 6 Mathematics 2320 Winter 2014
Due: March 7 , 2014 . SHOW ALL WORK
1. Show that each of the following functions is one-to—one and onto, and ﬁnd its inverse:
(a)A:{