## Algebra of real functions in math

List of Algebra of real functions Addition of two real functions Let f : X → R and g : X → R be any two real functions, where X ⊂ R. Then, we define (f + g): X → R by (f + g) (x) = f (x) + g (x), for all x … Read more

## Functions in set theory of math

A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B In other words, a function f is a relation from a non-empty set A to a non-empty set B such that the domain … Read more

## Relations in set theory of math

A relation R from a non-empty set A to a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B. The second element is called the image of … Read more

## Cartesian Products of Sets in math

Given two non-empty sets P and Q. The cartesian product P × Q is the set of all ordered pairs of elements from P and Q, i.e., P × Q = { (p,q) : p ∈ P, q ∈ Q } If either P or Q is the null set, then P × Q will … Read more

## Complement of a Set in math

Let U be the universal set and A a subset of U. Then the complement of A is the set of all elements of U which are not the elements of A. Symbolically, we write A′ to denote the complement of A with respect to U. Thus A′ = {x : x ∈ U and … Read more

## Difference of sets in math

Difference of sets The difference of the sets A and B in this order is the set of elements which belong to A but not to B. Symbolically, we write A – B and read as “ A minus B” Example Let A = { 1, 2, 3, 4, 5, 6}, B = { 2, … Read more

## Disjoint sets in math

If there is no common elements in sets then that sets are called disjoint sets. in other word If A and B are two sets such that A ∩ B = φ, then A and B are called disjoint sets For example, let A = { 2, 4, 6, 8 } and B = { … Read more

## Intersection in set of math

The intersection of two sets A and B is the set of all those elements which belong to both A and B. Symbolically, we write A ∩ B = {x : x ∈ A and x ∈ B} venn diagram of intersection Some Properties of Operation of Intersection A ∩ B = B ∩ A … Read more

## Union in set theory

The union of two sets A and B is the set C which consists of all those elements which are either in A or in B (including those which are in both). In symbols, we write. A ∪ B = { x : x ∈A or x ∈B } Venn diagram of Union Some Properties … Read more

## Operations on Sets theory

There are following operations on sets Union of sets Union of sets Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and all the elements of B, the common elements being taken only once. The symbol ‘∪’ is used … Read more