Ordered Pairs and Equality of an Ordered Pairs

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 ∈…

Complement of a set Let U be the universal set and let A be a set such that A ⊂ U. Then the complement of A with respect to U is denoted by A’ or Ac or U-A and is defined the set of all those elements of U which are not in A. Thus…

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

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…

Subsets of the set R of real numbers Following sets are important subsets of the set R of all real numbers:        (i)  The set of all natural numbers N = { 1, 2, 3, 4, 5, 6,…. }      (u)  The set of all integers Z =  { … – 3, – 2, -1,…

Macroscopic and Microscopic Approaches The behaviour of matter can be studied by two approaches 1. Macroscopic approach,                             2. Microscopic approach 1. Macroscopic approach – In the macroscopic approach a certain quantity of matter is considered for study without knowing the behaviour of individual…