Math 224 - Foundations - Dr. McLoughlin - Worksheet 1AA
Spring of 2013
Worksheet 1AA
Dr. M. P. M. M. McLoughlin
Questions and Exercises
Problems 1 - 25. Let U be the well dened universe N9 .
Let A = cfw_x|x < 4 Let B = cfw_x|p N9 x = 2 p, C = B c ,
D = cf
Math 224 - Foundations - Dr. Mc Loughlin - Worksheet 10
Spring of 2013
Worksheet 10
Dr. M. P. M. M. Mc Loughlin
Questions and Exercises
Let U = R R
1. Consider the permutation function p : N6 N6 dened by:
(
)
123456
365421
and the permutation function q :
Math 302, Dr. McLoughlin, Worksheet I, page 1 of 3
MATH 224
FOUNDATIONS
Dr. McLoughlin
Spring 2011
Worksheet 3
2.3
Prove or disprove the following claims:
1. 9 4 is a multiple of 5 n
n
n
( 2n 1)
2(n 2) is divisible by 7 n
( 2n 1)
2 (n 2) is divisible
MATH 224
FOUNDATIONS
WORKSHEET 2
DR. M. P. M. M. MCLOUGHLIN
1. Draw a Venn Diagramme that illustrates for any two sets A and B:
A BC
2. Draw a Venn Diagramme that illustrates for any two sets A and B:
AB
3. Draw a Venn Diagramme that illustrates for any
Math 224 Dr. McLoughlins Class Worksheet 12, page 1 of 1
BASIC CLAIMS AND EXERCISES ABOUT RELATIONS
ACCOMPANYING HANDOUT 12 2010 - 2
Do exercise 2, 3, 4 page 1 handout 13.
For sets let U = and for product sets let V = .
Exercise 12 2 1: Let U = . Let A =
Math 224 Dr. McLoughlins Class Worksheet 12, page 1 of 1
BASIC CLAIMS AND EXERCISES ABOUT RELATIONS
ACCOMPANYING HANDOUT 12 2010 - 1
Claim 12 -2: Definition 12-8 and alternate Definition 12-8 are logically equivalent.
Homework: prove or disprove the claim
Math 224 -
Dr. McLoughlin
- Worksheet 7 Spring 2011
Worksheet 7
Relations: Partial Orders, etc.
Dr. M. P. M. M. McLoughlin
Spring 2011
Exercise 14.1 : Let the universe be U = R R. Let the sets A = N3 , B = Z , C = N , and D = N5 .
3
4
14.1.1: Let P U
P =
Math 224 -
Dr. McLoughlin
- Worksheet 6 Spring 2011
Worksheet 6
Relations: Inverses, Compositions, etc.
Dr. M. P. M. M. McLoughlin
Spring 2011
Def. 14.1 : Let the universe be U = R and let k R. Dene the set Z be dened as
k
cfw_x : x Z |x| k .
For example,
Math 224 -
Dr. McLoughlin
- Worksheet 5
Spring 2011
Worksheet 5
Product Sets
Dr. M. P. M. M. McLoughlin
Spring 2011
We started this section of the course building from sets to the more general product sets.
Recall: Let U be a well dened universe. Let V be
Math 224 -
Dr. McLoughlin
- Worksheet 8 Spring 2011
Worksheet 8
Tues. - Thurs. Class Relations: Partial Orders, etc.
Dr. M. P. M. M. McLoughlin
Spring 2011
Exercise 14.1 : Let the universe be U = R R. Let the sets A = N4 , B = Z , C = N , and D = N5 .
3
3
Math 224 -
Dr. McLoughlin
- Worksheet 9
Spring 2011
Worksheet 9
Fun With Functions
Dr. M. P. M. M. McLoughlin
Spring 2011
We started this section of the course building from sets, power sets, collections, to the more general product sets; then to relation
Math 224 Dr. McLoughlin Worksheet 2, page 1 of 2
FOUNDATIONS OF MATHEMATICS
DR. MCLOUGHLINS CLASS
SPRING 2011
WORKSHEET 2
EXERCISE SET 1.2
1. Learn at least some of the ways to translate the conditional and biconditional from handout
one.
2. Memorise the
Math 224 - Foundations - Dr. McLoughlin - Worksheet
Spring of 2009
Worksheet I
Foundational Concepts
Dr. M. P. M. M. McLoughlin
Spring 2009
Denition: R = cfw_x| where x is a point on the line.
Let U = R for the line and let U = R R for the plane.
Denition
Math 224 - Foundations - Dr. Mc Loughlin - Worksheet 11
Spring of 2013
Worksheet 11
Dr. M. P. M. M. Mc Loughlin
Questions and Exercises
Let U = R R
1. Consider the function f : N R dened by:
f (x ) = 3 x 2 + 1
A. Prove or disprove f is injective
B. Prove