Mathematical Pre-requisities

Set:-
           Set is a collection of object without repetition and each object of set is called element of a set example D={x/x is a day of week}
Properties
1) Empty set  - It contains no elements denoted by ∅ {}.
2) Subset -  Set A is subset of B if every element in set A is in B denoted as A ⊂ B.
3) Equal sets -Two sets are equal if A ⊂ B and B ⊂ A..
4) Power set -A is a power set if 2^A.Set of all subsets A
        For example if,
           A={1,2,3}
           2^A={ {∅},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3} }
          2³=8 elements.
5) Compliment A' such that A'={x/x ∉ A}.
6) Union - A U B is all the elements in set A and B.
7) Intersection -A ∩ B is the element s both which is in A  and also in B.
8) Cardinality is the number of sets.


Relation :-  A relation R in set S is collection of ordered pair of elements in S.
Properties :-
1) Reflexive  -R is reflexive in S if xRx ∀ (for all) x ∈ S.
2) Symmetric -R is symmetric in x if xRy ⇒ yRx
3) Transitivie - R is transitive in x if xRy and yRz ⇒xRz
4)Equivalence relation -If relation is all three reflexive,symmetric and transitive.