By : Fridgo Tasman, S.Pd., M.Sc.. A Set is a simply collection of distict objects. The objects can...

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Set, Linear Function, Linear Equation and Modelling Economic Problem in Linear Equation System By : Fridgo Tasman, S.Pd., M.Sc.

Transcript of By : Fridgo Tasman, S.Pd., M.Sc.. A Set is a simply collection of distict objects. The objects can...

Page 1: 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,

Set, Linear Function, Linear Equation and Modelling

Economic Problem in Linear Equation System

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

Page 2: 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,

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

Page 3: 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,

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

Page 4: 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,

2. Description

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

Page 5: 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,

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

Page 6: 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,

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.

Page 7: 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,

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

Page 8: 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,

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

Page 9: 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,

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

Page 10: 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,

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

Page 11: 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,
Page 12: 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,

1. The commutative law of union and intersection

Laws of Set Operation

Page 13: 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,

2. The associative law of unions and intersection

Page 14: 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,

3. The distributive law of union and intersection

Page 15: 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,

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

Page 16: 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,

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

Page 17: 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,

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

Page 18: 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,

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

Page 19: 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,

Thank you