Set:

A set is a precise group of distinct objects. Well-defined group means that there exists a principle with the help of which it is probable to tell whether a provided object relates or does not belong to related collection. Usually sets are shown by capital letters A, B, C, X, Y, Z etc.

Representation of a set

Generally, sets are shown in the subsequent ways

Roaster form or tabular form

In that form, we define all the member of the set within braces (curly brackets) and distinguish these by commas. For example, the set of all even integer numbers less than 10 and bigger than 0 in the roster form is defined as: A = {2,4, 6,8}

Set builder form or rule form

In that form, we write a variable (say x) showing any member of the group or set followed by a property fulfilled by each and every member of the set. A = {x| x ≤ 5, x ∈ N} the symbol '|' define for the words" such that".

Relaitons:

Suppose A and B be two non-empty sets then every subset of A x B describes a relation from A to B and each relation from A to B is subset of A x B.

Consider R⊆A x B and (a, b) ∈ R. then we can say that a is associated to b by the relation R and write it as  a R b. If (a, b) ∉ R, we write it as ab.

Example Let A {1, 2, 3, 4, 5}, B = {1, 3}

We set a relation from A to B as: a R b iff a ≤ b; a ∈ A, b ∈ B. Then

     R ={(1, 1), (1, 3), (2, 3), (3, 3)} ⊆ A x B

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