# Applied Mathematics: Set Theory

Well congratulations to all the new commerce students, because you got lucky with the introduction of applied mathematics subjects in your curriculum. This subject is useful for all the commerce students as it includes those topics which will be useful according to your stream subjects.

I will try my level best to sail you through this new subject with a whole new curriculum. Let’s start with **Algebra**, one of my favorite topics, and under algebra, I am going to discuss **‘Sets Theory‘.**

Now, what do we mean by sets? Well, it is a collection of ‘well-defined’ objects. When we say, ‘well-defined’ it means the answer will remain the same to the question asked. For example, if I ask you, How many players are there in any Indian cricket team? What will be your answer? Yes, its 15 players, not 11. So, in this case, the correct answer will remain the same.

Now, if I ask you, tell me the name of all the ‘best players’ of the Indian cricket team? Hmmm, the answer will vary because there is no universal answer for everyone’s preference.

We always represents set with capital letters of alphabets with ‘{‘ bracket. For example, set A= {all vowels}. This can be re-written with its elements like, A= {a,e,i,o,u}, here ‘a,e,i,o,u’ are elements of sets.

**Lets discuss two important rules of writing any set:**

**Rule 1**– Elements will be written once only. For example, if I ask you to write elements of the word ‘INSTITUTE’ in a set, then you will write letters only once without repetitions. Like this, {I,N,S,T,U,E}. As you can see, I have not repeated any letter in this set. Try writing set for the word ‘MISSISSIPPI’ and drop me an email on Contact@LearnWithAnjali.com**Rule 2**– Order does not matter while you are writing a set. I will repeat the word ‘INSTITUTE’ and while writing it in a set form, the order of the letters does not matter, {S, N, I, T, U, E}.

**To summarize, sets theory tells you the well-defined and universal answer to all the questions. It does not apply to the topics where there is no unique answer.**

Photo by Crissy Jarvis on Unsplash