Open Interval

Domain of relation Let R be a relation from a set A to a set B. Then the of all first components or coordinates of the ordered pairs belonging to R is called the domain of R. Thus, domain of R = { a : (a, b) ∈ R} Clearly, domain of R ⊆  A…

Universal set In any discussion in set theory, there always happens to be a set that contains all sets under consideration i.e. it is a super  set of each of the given sets. Such a set is called the universal set and is denoted by U. Thus a set that contains all sets in 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 ∈…

Intervals as subsets of R    Closed intervals  Let a and b be two given real numbers such that a < b. Then the set of all real numbers x such that a ≤ x ≤ b is called a closed interval and is denoted by [a, b] .   Thus,     [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…

Symmetry difference of sets Let A and B be two sets. The symmetry difference of sets A and B is the set (A-B) ∪ (B-A)  and it is denoted by A ∆ B. Then A∆B=(A-B) ∪ (B-A) = {x : x ∉ A ∩ B}. In Fig 9 shaded region represents A∆B Fig (9) Example…