Table of Contents

**MTH001: Elementary Mathematics**

Elementary math includes topics from algebra, analysis, mathematics, mathematics, geometry, and numerical theory commonly taught at the elementary or high school level. MTH001 Handouts pdf

#### MTH001 Handouts pdf

**Course Category: Mathematics **MTH001 Handouts pdf

**Course Outline**

Logic, Truth Table, Logic Equivalence, Laws of the Algebra of Propositions, Translating Word Statements to Symbolic Notation & Vice Versa, Bi-Conditional Statements and their Equivalence, Arguments, Valid and In Valid arguments, Sets, Venn Diagram and Membership Table, Operations on sets, Venn Diagrams for operations on sets, Ordered Pairs, Relations and Matrix Representation of a matrix, Types of relations and Directed graph, Irreflexive and antisymmetric relations and partially ordered relations, Functions, Domain Codomain and Range, Types of function, Sequence, Arithmetic, and Geometric Sequence, Series, Sum of Arithmetic and Geometric Series, Performing basic arithmetic operations using Microsoft Excel, Basic calculations of percentages and investments using Microsoft Excel, MTH001 Handouts

Discount, Simple and compound interest, Average due date, Annuity, Accumulated value, Accumulation Factor, Discount Factor, Discounted value, Matrix, its Dimension and Types of a matrix, Operations on Matrices, Merchandising, Introduction to Statistics, Data Representation, The Central Tendency of a data-set, Median, Empirical Relation, Quartiles, Geometric mean, Harmonic mean & relationship between them, Measures of Dispersion, Mean Deviation, Standard Deviation and Variance & Coefficient of variation, Permutations, Combinations, Definitions of Probability, Relative Frequency, Axiomatic Definition & Laws of Probability, Independent and Dependent Events, Multiplication Theorem & Marginal Probability.MTH001 Handouts pdf

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### MTH001 HANDOUTS

**MTH001: Elementary Mathematics**

#### What is Discrete Mathematics?

Discrete Mathematics is about processes that include the sequence of each step.

#### LOGIC

It makes sense to study the principles and methods that distinguish between valid and wrong arguments.

#### SIMPLE STATEMENT:

A statement is a declaration that is true or false but not both. The statement is also called a proposal Example: 2 + 2 = 4, It is Sunday today If the proposal is true, we say it has a true value of “truth” If the proposal is false, its true value is “false.” The truths “truth” and “falsehood,” respectively, are defined by the letters T and F.

##### EXAMPLES:

1. The grass is green.

2.4 + 2 = 6

2.4 + 2 = 7 3 ..

There are four fingers on the hand, suggestions. MTH001 Handouts pdf download

#### COMPOUND STATEMENT:

Simple statements can be used to create an integrated statement.

#### STRATEGIC CONNECTIONS:

##### EXAMPLES

1. “3 + 2 = 5” and “Lahore a city in Pakistan”

2. “Green Grass” or “Hot Today” 3. “Discrete Mathematics is not hard for me” AND, OR, NOT called LOGICAL CONNECTIONS.

#### NEGATION (~):

If p is a variation of the statement, then the contradiction of p, “not p”, is defined as “~ p”. if p is false, ~ p is true.

**CONJUNCTION **(∧):

If p and q are statements, then the conjunction of p and q is “p and q”, defined as “p ∧ q”. It is true there, and only when, both p and q are true. If p or q is false, or both are false, p∧q is false.

**DISJUNCTION (****∨****) OR INCLUSIVE **

If p and q are statements, then the division of p and q is “p OR q”, defined as “p ∨ q” is true if at least one of the p or q is true and only false when both p and q. they are false. Note that table F is in that line only when both p and q have F and all other T values. So in order to find the true values of the separation of the two statements, we will first look for where both statements are false. then write F in the corresponding column in p ∨ q column and in all other lines we will write T in the p ∨ q column.

**VALID AND INVALID ARGUMENT: **

The contradiction applies if the conclusion is true when all the structures are true. Alternatively, an argument is permissible if the combination of its structures suggests a conclusion. Namely (P1∧ P2 ∧ P3 ∧.. ∧ Pn) → C tautology. Arguments are not valid if the conclusion is false when all the structures are true. Alternatively, an argument is invalid if the merger does not imply an end result.

##### EXAMPLE:

Indicate that the following argument form is valid: p → q

p ∴ q

#### SETS

A well-defined collection of {distinct} objects is called a set. ¾ Objects are called elements or members of a set. ¾ Sets are defined by the letters A, B, C…, X, Y, Z. ¾ The elements of a set are represented by lowercase letters a, b, c,…, x, y, z. ¬A, which reads “x ¾ If the object x is a member of set A we write x ¬A, A” or “x is A” or “x is an A element”, otherwise we write x which reads “x not A ”or“ x is not A ”or“ x is not part of A ”.

**TABULAR FORM**

Lists all features of a set, comma-separated and enclosed in parentheses or in brackets {}. EXAMPLES

In the following examples, we write sets in Table Form.

A = {1, 2, 3, 4, 5} is a set of the first five natural numbers

. B = {2, 4, 6, 8,…, 50} is a set of equal numbers of up to 50.

C = {1, 3, 5, 7, 9…} is a set of odd deposit numbers.

#### MEMBERSHIP TABLE

A table showing the membership of items by sets. To indicate that an object is in a set, using 1; to indicate that an item is not in the set, using 0.

#### ORDERED PAIR

The formal pear (a, b) contains two elements “a and” b is the second element. ”And“ b ”where“ a ”is the first element a = c and b = d. b, s a = b. XERC SE: Orders ordered (a, b) and (c, d) are equal if, and only if a = c and b = d.