a) Set: A Set is any well defined collection of distinct objects.
E.g C = {4, 2, 1, 3} and D = {blue, white, red}are sets of natural numbers and set of colors respectively.
b) Element of Set: A number, letter, item or any other object contained in a Set is called Element of a Set. In a) above, elements of Set C are 1,2,3 and 4.
c) Order of a Set: are special binary relations. Suppose that P is a set and that ≤ is a relation on P, Then ≤ is a partial order if it is reflexive, antisymmetric and transitive.
d) Null Set: is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Common notations for the empty set include "{}", " ", and " ".
e) Finite Set: a finite set is a set that has a finite number of elements. For example, is a finite set with five elements. The number of elements of a finite set is a natural number (non-negative integer),and is called the cardinality of the set. A set that is not finite is called infinite. For example, the set of all positive integers is infinite:

f) Proper Subset: A proper subset is a grouping of numbers in which all the numbers for two quantities have the same numbers, but are not equal.

g) Data: are values of qualitative or quantitative variables belonging to a set of items.

h) Statistics: Statistics is a branch of mathematics that deals with the collection, organization and interpretation of data.
i) Probability: is a measure or estimation of how likely it is that something will happen or that a statement is true. Probabilities are given a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen). The higher the degree of probability, the more likely the event is to happen, or, in a longer series of samples, the greater the number of times such event is expected to happen.
j) Event: is a set of outcomes to which a probability is assigned.
k) Mutually Exclusive Events: Two events are 'mutually exclusive' if they cannot occur at the same time. An example is tossing a coin once, which can result in either heads or tails, but not both.
l) Independent Event: Two events are said to be independent if the occurrence of one does not affect the probability of the other. Two events A and B are independent if their joint probability equals the product of their probabilities: .
m) Random Experiment: Experiments which do not always yield the same result even when repeated under the same conditions.
n) Intersection of Sets: the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements. The intersection of A and B is written A ∩ B.