Ordered Pairs and Equality of an Ordered Pairs
Ordered pairs
An ordered pairs consists of two objects or elements in a given fixed order.
For example, if A and B are any two sets, then by an ordered pair of elements we mean a pair (a, b) in that order, where a ∈ A, b ∈ B.
NOTE
An ordered pair is not a set consisting of two elements. The ordering of the two elements in an ordered pair is important and the two elements need not be distinct.
Example
The position of a point in a two dimension plane in cartesian coordinate is represented by an ordered pair. Accordingly, the ordered pairs (1, 3),(2, 4),(2, 3) and (3, 2) represents different points in a plane.
Equality of an ordered pairs
Two ordered pairs (a1, b1) and (a2, b2) are equal iff (if and only if) a1=a2 and b1=b2.
i.e. (a1, b1) = (a2, b2) ⇔a1 = a2 and b1 = b2
It is evident from this definition that (1, 2) ≠ (2, 1) and (1, 1) ≠ (2, 2).
∈ R, a ≤ x < b are known as semi-open or semi-closed intervals . (a,…