Algebra: Ordered Pair and Cartesian Product

Notes

Relation

A relation between two sets is a collection of ordered pairs containing one object from each set. If the object x is from the first set and the object y is from the second set, then the objects are said to be related if the ordered pair (x,y) is in the relation. A technical definition of a function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. This means that if the object x is in the set of inputs (called the domain) then a function fh

Ordered Pair

A pair of numbers which always follows a rule that the first components should always be X-component and the second component should always be taken from Y-component, where the pair must be always enclosed within small brackets () and separated by a common is known as an ordered pair. Two ordered pairs are said to be equal if and only if their corresponding components are equal. The Cartesian Product between two sets is the set of all possible ordered pairs with the first element from the first set and second element from the second set.

Function

A function is a special relationship where each input has a single output. This note includes all the notes of function including its types, features and the way of representation.