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