## Convenience Sampling

When you take samples on the basis of your comfort, it is called convenience sampling. The name “convenience” sampling is given because the selection of samples is done without any predetermined theories or principles. Convenience sampling is not preferred way of sampling for effective analysis as samples are taken from specific section of the population. Convenience sampling is a type of Non-probability Sampling.

## Systematic Random Sampling

While reaching to conclusion about a large volume of data, we prefer to take samples from the whole population and then we analyze them and reach to a conclusion. We expect that the samples taken represents the whole population sufficiently or at least reasonably.

## Stratified Random Sampling

When we select a limited number of elements from large group of elements (population) for sampling, we want to make sure that the samples taken correctly represent the population. How much our analysis of the limited dataset agrees with the characteristics of the population depends largely on the method of sampling used.

Introduction Suppose that we are going to find out how many of the audience of the ‘Real Madrid vs. Barcelona’ match that was conducted on October 2014 like Lionel Messi the most and how many of them bet on Neymar Júnior as the best footballer in the world. It is a herculean task to collect the exact data by assessing the views of all the 400 million audience.

When we choose certain items out of the whole population to analyze the data and draw a conclusion thereon, it is called sampling. The way of sampling in which each item in the population has an equal chance (this chance is greater than zero) for getting selected is called probability sampling. Probability Sampling uses lesser reliance over the human judgment which makes the overall process free from over biasness.

Suppose you have to run a survey about the coffee drinking habits of high school students of USA. The population of the students is about 4 million. You can not even imagine running the survey by asking each and every student to get the relevant data because of requirement of huge amount of time, money and other resources. The cost of the survey in this case would be too monumental to justify the effort. To solve these types of problem, sampling can be used.

## Complement of Sets

Complement of a set A, denoted by Ac, is the set of all elements that belongs to universal set but does not belong to set A. In mathematical form, complement of a set can be expressed as:

## Cartesian Product

For two sets A and B, the Cartesian product of A and B is denoted by A×B and defined as: A×B = { (a,b) | aϵA and bϵB } Cartesian Product is the multiplication of two sets to form the set of all ordered pairs. The first element of the ordered pair belong to first set and second pair belong the second set. For an example,

## Terminologies Related to Sets

There are many technical terminologies that we need to understand to improve our learning of set theory. Some of them are explained below:

## Set Notation

A set is a collection of distinct objects(elements) which have common property. For example, red, blue, and green are colors. When the elements are considered collectively, set is formed. The elements in a set can be represented in a number of ways, some of which are more useful for mathematical treatment and others for general understanding. These different methods of describing a set are called set notations.