Module 1 - Home
Foundations: Logic and Proofs
Modular Learning Outcomes
Upon successful completion of this module, the student will be able to satisfy the following
outcomes:
Case
o Demonstrate mastery of basic concepts and principles of propositional log

1
BASIC COUNTING RULES
Proposition 1.1 (Product Rule) If something can happen in n1 ways,
and no matter how the first thing happens, a second thing can happen in
n2 ways, and so on, no matter how the first k 1 things happen, a k-th
thing can happen in nk

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Tautologies, contradictions and contingencies
Consider the truth table of the following formula:
()
p
(p p)
If you look at the final column, you will notice that the truth value of the whole formula depends
on the way a truth v

2.1
2.1
Simple & Compound Propositions
1
Simple & Compound Propositions
Propositional Logic can be used to analyse, simplify and establish the equivalence of statements.
A knowledge of logic is essential to the study of mathematics. In order to prove theo

Introduction to sets http:/www.mathsisfun.com/sets/sets-introduction.html
Introduction to Sets
Forget everything you know about numbers.
In fact, forget you even know what a number is.
This is where mathematics starts.
Instead of math with numbers, we wil

Case 1 Assignment
Answer each question completely, including all lettered parts.
1. Which of these sentences are propositions? What are the
truth values of those that are propositions?
a) Miami is the capital of Florida.
b) 2 + 3 = 5.
c) 5 + 7 = 10.
d) x

Set operations
http:/www.cs.odu.edu/~toida/nerzic/content/set/set_operations.html
Set Operations
Subjects to be Learned
union of sets
intersection of sets
difference of sets
complement of set
ordered pair, ordered n-tuple
equality of ordered n-tuple

Case 2 Assignment
1. Suppose that A = cfw_2, 4, 6, 8, B = cfw_2, 4, 8, and C = cfw_4, 8. Write out the relationship
between A and B, A and C, B and C.
2. Determine whether each of the following pairs of sets are equal.
a) cfw_1, 3, 5, 7 and cfw_3, 1, 7, 5

Counting Principles:
https:/people.richland.edu/james/lecture/m116/sequences/counting.html
7.6 - Counting Principles
Each branch of mathematics has its own fundamental theorem(s). If you
check out fundamental in the dictionary, you will see that it relate