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Difference of sets Let A and B be two sets. The difference of A and B written as A – B, is the set of all those elements of A which do not belong to set B Thus A – B={ x : x ∈ A and x  ∉ B} or  A – B={ x…

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…

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…

Laws of algebra of set THEOREM 1 (Idempotent Laws) For any set A (i) A ∪ A = A (ii) A ∩ A = A PROOF  (i) A ∪ A= { x : x ∈ A or x ∈ A} ={x : x ∈ A} = A    (ii) A ∩ A = {x : x…

Relation Let A and B be two sets. Then a relation from set A to B is a subset of A × B. Thus, R is a relation from A to B⇔R ⊆ A × B. If R is a relation from a non-void set A to non-void set B and my if (a, b)…

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…

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…

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…

Function as a set of ordered pairs     Let  A and B be two non-empty sets. A relation f from A to B i.e   a subset of A × B is called a function (or a mapping or a map) from A to B, if i) for each a ∈ A there  exists b ∈ B…

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…