Set, Linear Function, Linear Equation and Modelling

Economic Problem in Linear Equation System

By : Fridgo Tasman, S.Pd., M.Sc.

A Set is a simply collection of distict objects.

The objects can be person, number, food, and something else. Therefore, all the students enrolled this course can be considered as a set.

The objects in a set are called the elements of set ( )

Set

1. EnumerationIf we let S represent of four number 2,4,6, and 8. We can write by enumeration of element by

Two alternative ways of writing a set

2. Description

if we let L denoted the set of all positive intergers. Enumeration became difficult therefore we can write

1. Equalif two sets S1 and S2 happen to contain identical element for example

Then S1 and S2 are said to be equal (S1 = S2 )

Relationship between Set

2. Subsetone set might be a subset of another set. If we have two sets

then S is subset of T, because every element in S is also an element of T.

More formal element of that S is a subset of T, if and only if

Using the set inclusion symbols Ϲ (is contain in) and Ↄ (includes) we may then write

S Ϲ T or T Ↄ S

1. UnionTo take union of two set A and B means to form a new set containing those element (And only those elements),belonging to A, to B or both A and B. The union set is symbolized by For Example :

Operation on Set

2. IntersectionThe intersection of two sets, A and B, is a new set which contain those element (and only those elements),belonging to both A and B. The intersection set is symbolized by

For Example: if A and B that defined in previous page, then we have

3.Complement of a SetIf we talk about complement of set,we have to know the universal of set. If we defined the universal of set and we have set therefore we can know the complement of A is

1. The commutative law of union and intersection

Laws of Set Operation

2. The associative law of unions and intersection

3. The distributive law of union and intersection

What is Function?

y is said to be a function of x which is denoted as y = f(x)

If any x value uniquely determine a y valueTherefore it will make a set of ordered pairs which satisfy the property.

Linear Function

Linear Function is functions that have x as the input variable, and x has an exponent of only 1.

Can be denoted as y=mx + b. Example of Linear Function

y=4x+7,y=11x-10 and etc

Linear Function

If we ‘strict’ the value of y in linear function, it will make linear equation. Therefore we can defined linear equation as the equation which has x exponent of only 1.For Example : 7x + 5 = 8,

12x + 5 = 19 and etc

Linear Equation

Linear Equation System is a colection of Linear equation.There are several ways to solve linear equation system:1. Graph Method2. Subsitusion Method3. Elimination Method and4. Determinant Method

Linear Equation System

Thank you