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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 ∈…

Types of relation Void relation:- Let A be a set. Then, Φ ⊆ A x A and so it is a relation on A. This relation is called the void or empty relation on set A.                    In other words, a relation R on a set A is called void or empty relation, if no element…

Venn diagrams The diagram drawn to represent sets are called Venn-diagram. In Venn-diagram the universal set U is represented by points within the rectangle and its subsets are represented points in closed curves (usually circles) within the rectangle. If a set A is a subset of a set B, then the circles representing A is…

Function as a correspondence   Let A and B be two non-empty sets. Then a function ‘f ‘ from set A  to set B is a rule or method or correspondence which associates elements of set A to elements of set B such  that: Fig. 2(a) (i) all elements of set A are associated to…

Semi-Open or Semi-Closed interval If a and b are two real numbers such that a < b, then the sets (a, b] = { x : x ∈ R, a < x ≤ b}  and  [a, b)={ x 😡 ∈ R, a ≤ x < b  are known  as  semi-open  or  semi-closed intervals . (a,…

Union of sets Let A and B be two sets. The union of A and B is the set of all those elements which belong either to A or to B or to both A and B. We denote A union B by notation “A ∪ B” Thus  A∪B = { x : x ∈…