Boolean Algebra Project
Levi Kilgore
1. What is a Boolean Variable?
Boolean algebraisasetofrulesandoperationsforworkingwithvariableswhosevalues
areeither0or1.Thevalue1correspondstoTintherulesofpropositionallogic,andthevalue
0correspondstoF.
2. Create a ta
Number Theory Lecture
Discrete Math
A small explanation about truth tables.
Find the truth table of (p v q) ^ (p v r)
We have three variables (p, q and r are the variables; If a variable is repeated, do
not count it more than once), so we need 8 rows.
P Q
Combinatorics Lecture
Discrete Math
Combinatorics: This is counting, and counting big numbers.
Product Rule (Multiplication Principle): If you have to select one element of a set,
and a bunch of sets, the number of possible combinations between all sets i
Discrete Math
Logic 1 Lecture
This session is being recorded, and it will be posted as an announcement later
tonight or tomorrow morning. At the same time, I type a lot of notes, and the notes
will be available right after the session is completed, and it
Sequences, Summations and Matrices
Discrete Math
Sequences: List of numbers, organized by positions.
A1 = 2
A2 = 4
A3 = 7
A4 = 0
A5 = 3
A6 = 10
Note: Sequence An contains more numbers in the list, but I am only showing the
first 6 terms.
What number is in
6.2.2
[(76 mod 7) (58 mod 7)] mod7
Step 1: To find mod 7 think about a clock. If the number is positive it goes clockwise, if it is
negative it goes counter clockwise.
So, we are going to start a number line because I cant draw a clock starting with 0 you
Simple Truth table for 2 propositions (p, q):
Conjunction and Disjunction of 2 propositions (p, q)
Conditional and Biconditional Statements for 2 propositions (p, q)
Examples for compound statements when dealing with 3 propositions (p,q,r):
Showing that t
B: (P ^ Q ^ R) v (P ^ Q ^ R)
C: (P v Q v R) ^ (P v Q v R) ^ (P v q v R)
P Q R P Q R (P^Q^R) (P^Q^R) G v H (PvQvR) (PvQvR)
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
F
T
F
T
F
T
F
F
F
F
F
T
T
T
T
F
F
T
T
F
F
T
T
F
T
F
T
F
T
F
T
F
T
F
F
F
F
F
F
F
F
T
F
F
F
F
F
F
T
T
1.1|Fundamentals:Logic
Test in WEEK 1 : LOGIC
2
FEB
STATUS
1
Isthestatement,"Donotpassgo."alogicalproposition?
10Points
YesanditisTrue
YesanditisFalse
No,itisnotalogicalproposition.
2
Isthestatement,"Thissentenceisfalse"alogicalproposition?
10Points
Yesan
Set Theory
APPLYING LAWS OF LOGIC TO GROUPS
A GROUP IS A SPECIAL TYPE OF SETWE WONT GO OVER THOSE HERE
Why Set Theory?
Applying logic to entire
groups
Players on a Team
Players part of Offense
Injured players
An important foundation for
other mathematical
Number Theory
NO DECIMALS ALLOWED!
Why Number Theory?
There are lots of scenarios where calculations and values need to
be presented in integer values
Time: (Hours, Minutes, Seconds, Milliseconds, etc)
Needed to automatically updated your phone, computer
Combinatorics
YOU LEARNED TO COUNT AS A CHILD
NOW LEARN TO COUNT LIKE AN ADULT!
What we already know
Cardinality
Count how many elements belong to a set
Length of a Sequence
Is the sequence Finite or Infinite?
The last index first index + 1
Counting
Logic I
THE FOUNDATION OF ALL MATHEMATICS
AND
THE KEY TO THE LANGUAGE OF MACHINES
Why we start with Logic
THE MOST CRITICAL SKILL TO FUTURE
TECHNOLOGY DRIVEN COURSES
LOGIC REQUIRES NO PRE-REQUISITE MATH
COURSES
EARLY PRESENTATION ALLOWS FOR
REPETITION OF
Sequences, Summations, and
Matrices
INDEXED DATA STRUCTURES
Why These Topics?
While sets are a good way to view collections of data in the
abstract actual implementation on computing devices
requires requires more structure.
Databases
Inventory
Program
Functions
THEY DO A THING
Why Functions?
Functions serve an important role in both
mathematics and programming
Calculations that are plug and chug operations will
be presented as functions
You will be learning about and using pre-defined
functions in pr