Set and Elements

a set is a collection of distinct objects, considered as an object in its own right. For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2,4,6}.

an element, or member, of a set is any one of the distinct objects that make up that set

A number, letter, point, line, or any other object contained in a set.

There are two ways of describing, or specifying the members of, a set. One way is by intensional definition, using a rule or semantic description. See this example:

A is the set whose members are the first four positive integers.

B is the set of colors of the French flag.

The second way is by extension, that is, listing each member of the set. An extensional definition is notated by enclosing the list of members in braces:

C = {4, 2, 1, 3}

D = {blue, white, red}

Definition (Equality of sets): Two sets are equal if and only if they have the same elements.

(Subset): A set A is a subset of a set B if and only if everything in A is also in B.

two sets are said to be joint or overlapping sets ,if they have atleast one element in common

a universal set is a set which contains all objects, including itself

Intersection of Sets is defined as the grouping up of the common elements of two or more sets.

Combining all the elements of any two sets is called the Union of those sets.

Union of two sets A and B is obtained by combining all the members of the sets and is represented as A ∪