This document outlines the topics covered in several lectures on discrete mathematics. It introduces key concepts like propositions, truth tables, logical expressions, sets, functions, integers, prime numbers, and rules of probability. Examples and practice problems are provided for topics like logical equivalence, quantifiers, function composition, greatest common divisors, and the product and sum rules. Later lectures will cover more advanced topics such as encryption techniques, the inclusion-exclusion principle, and permutations and combinations.

1. Discrete Mathematics
Lecture:01
1) Definition of discrete mathematics.
2) Benefits of discrete mathematics.
3) Distinguish between mathematics & logic.
4) What is proposition? Example
5) Truth tables of the followings.
I. Negation(NOT)
II. Conjunction(AND)
III. Disjunction(OR)
IV. Executive OR
V. Bioconditional
VI. Implication.
6) Converse, Contra positive, & inverse?
Lecture:02
1) Translating English sentences into logical expression & translating logical
expression into English sentences.
I. Example
II. Class practice
2) Logical equivalence
I. Definition
*How to provelogical equivalence.
II. Class practice
III. Home work
Lecture:03
1) Tautology, contradiction, & contingency
I. Example
II. Class practice

2. Lecture:04
1) Universal quantifiers
2) Existential quantifiers
I. Example
II. Class practice
Lecture:05
1) Function: Definition & uses
2) Types of function
I. One to one (not onto)
II. Onto (notone to one)
III. One to one & onto
IV. Neither one to one not onto
V. Not a function.
3) Composition of function
I. Definition
II. Class practice
New Chapter:
1) Integers & divisions
2) Division algorithm
I. if a ǀ b & a ǀ c, then a ǀ (b+c)
II. if a ǀ b, then a ǀ bc for all integer c
III. if a ǀ b & b ǀ c then a ǀ c
(1)Definition (2) Equal set (3) Empty set (4) Sub set ( 5) proper set (6) power set
(7) what is the power set of an empty set (8) Cartesian product(9) Venn-diagram
(10) Complement of a set (11) Disjointset (12) Rules of set.

3. Lecture:06
1) Prime number
I. definition
2) Prime factorization
II. Example
3) Greatest common divisor (GCD)
LowestCommon Multiple (LCM)
III. Example
IV. Home work
4) Cryptology
I. Encryption
II. Decryption
New chapter:
1) Productrule
I. Definition & class example
2) Sum rule
II. Definition & class example
Lecture:07
1) Combination of productrule & sumrule.
I. Class practice
2) Inclusion-Exclusion principle
II. Definition
III. Class practice
3) Permutation & combination.
I. Class practice