First I will explain the definition of what a set is. Before learning to count, children learn how to put objects into groups. It doesn’t matter what kinds of groups they are forming. It doesn’t matter if they are putting six pencils together or four pens. It’s all the same. In both situations children have just formed two sets. The first set has 6 elements and the second one has 4 elements. And they didn’t ever know about the theory of sets.

I have already understood what a set is, but how many subsets can I form?

Keep calm! First we have to say that a subset is a set that is within another set. Therefore, let’s suppose we have 3 pieces of fruit: a banana, an Orange and a strawberry, which naturally form a set which can be identified as it follows: Fruit={banana, orange, strawberry}. From this set I can form 3 sets having just one element, this is, {banana}, {orange} and {strawberry}. I can even form 3 sets containing two elements, this is, {banana, orange}, {orange, strawberry} and {banana, strawberry}. But we haven’t finished yet, since it is possible to form a set with all the elements: {banana, orange and strawberry} and finally it is even possible to form an empty set, which is represented like this: { }. So, from a set of three elements it was possible to form 8 different subsets.


But... Isn’t there any easier way instead of counting by hand?

Yes, there is. Fortunately there is a formula that immediately gives us the number of subsets present in a set. Let’s suppose that letter `n` stands for the number of elements of the set. So, to calculate the number of subsets you just have to solve `2^n`. In the example regarding the three kinds of fruits we would have `2^3=8`. In the above picture we have a set with the reference `A` which has 8 people. In this case it is possible to form 256 different subsets since `2^8=256`. It would be hard work if you had to count it by hand, wouldn’t it?

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