Ordered pairs can be explained as the collection of two objects. it is written in brackets “( )” and separated by a coma”,” in between. The two objects are called as coordinates, for instance let us consider the objects x and y, these objects can be written as (x, y) and these are plotted based on their coordinate values; x coordinate is on x-axis and y coordinate is on y-axis or it is simply written as “two numbers in a certain order’’.
General form of an ordered pair:
(x, y)
X is X- coordinate
Y is Y- coordinate
Example:
For example the number 1 and 2 can form an order pair as.
i) (1, 2)
ii) (2, 1)
And we can also form an order for same numbers
i) (4, 4)
ii) (3, 3)
Properties
• Let us take (a1, b1) and (a2, b2) as two ordered pairs the characteristic property to define them is
(a1, b1) = (a2, b2) if and only if a1=a2 and b1=b2
• We can also nest one of the ordered pair in an other ordered pair such that (a, (b, c)) and this can also be written as (a, b, c)
• If (a) is in set A and (b, c) is in set B then (a, (b, c)) is defined as B is subset of A.
Ordered Pairs, Set Theory
Set theory is a branch of mathematics which deals with sets. Sets are collection of similar objects. This theory includes the operations such as union (U) and intersection (?), the union of two sets is a set containing all the elements of both the sets and each listed only once. The intersection is the set of all elements common to both the sets.
(AUB) is set A is union of set B.
(A?B) it shows common values of set A and B.
Example:
Let us take two sets A and B
A : 1, 2, 3, 4, 5
B : 3, 4, 5, 6, 7
(A U B) = 1, 2, 3, 4, 5, 6, 7
(A ? B) = 3, 4, 5
Note: If any set is having ‘0’ numbers of elements then it is known as null set and denoted as ?.
Plotting an order pair
This is very important technique in ordered pairs that is to locate points on a graph. We plot a point on a graph considering the two numbers called coordinates (x-coordinate and y-coordinate). The x-coordinate lies on X-axis and Y-coordinate lies on Y-axis; these two axes are called as coordinate axes.
In the above graph the points are plotted by considering their respective x-coordinate and y-coordinate, the point (2, 4) is plotted based on their coordinate values ‘2’ and ‘4’ and the point (3, 2) is plotted based on the coordinates ‘3’ and ‘2’. A graph always starts from a point called origin; at this point the value would always be ‘0’ and it is denoted as (0, 0) and a diagonal which passes through origin combines all the points whose a and b values are same say(1,1) (2,2) etc.
Solved Problems
1. Draw the Venn diagram by considering information given below.
A : 1, 3, 5, 6, 7
B : 2, 3, 4, 5, 6, 8, 9
(A?B) = 3, 5, 6
Solution: Given,
A : 1, 3, 5, 6, 7
B : 2, 3, 4, 5, 6, 8, 9
(A?B) = 3, 5, 6
2. What is the relation between A and B.
A: 1, 2, 3, 4, 5, 6, 7, 8
B: 4, 5, 6, 7
Solution: Given that,
A: 1, 2, 3, 4, 5, 6, 7, 8
B: 4, 5, 6, 7
From the information given above we can say that
B is a subset of A
A and B are intersected.
(A?B) = 4, 5, 6, 7
3. Draw the graph for the equation y=8-x2
Solution: Given equation, y=8-x2
In the above graph the value of y is determined based on the x value.
Put x=1 y=8-1=7 so point is (1,7) and so on.
Related Tags
relations , coordinate-system , analytic-geometry