Subsets

A collection of things which have something in common as per the rule is called a set. For instance set of colors would be {red, green, yellow, white, blue} this set represents the collection of five different colors, these are called the elements of the set.

The elements are separated using commas (,) and every element is unique in the set. The notation uses parenthesis which are curly or in other words the flower brackets {} and usually a set is denoted using a capital letter.  Let ‘E’ be a set denoting all the even numbers less than ten; so set E={2,4,6,8}. While learning about sets we come across finite set, infinite set, universal set, empty set, sub-set and power set.

In this article we shall learn more about a Sub-set. Consider a set A={1,2,3,4,5,6} and set B={2,4,6}. When we compare both the sets it is clear that all the elements of set B are present in the set A and hence we can call set B as the sub-set of set A.

Definition of a Subset can be given as, a set B is a sub-set of the set A only if every element of set B is in the set A. The subset sign is ‘⊆’.

For instance, set A={orange, pineapple, apple, grapes, kiwi, mango} and set B={apple, kiwi, orange, mango}. Here each element of set B is in the set A and hence Set B is a sub-set of Set A and is denoted as B⊆A. Suppose Set P={2,3,4,5,8} and set Q={1,3,7,9}; each of elements of set Q are not in the set P and hence we cannot call set Q a sub-set of set P.
So, subset meaning is the set which is a part of the whole set.

So, a subset in math can be better explained using the following example, a set P is a sub-set of set Q if and only if all the objects or elements of set P is in set Q.

If set P={x, y, z} and set Q={x, y, z, p, q, r}, every element of P is in Q and hence P⊆ Q. Some of the subsets examples are, list of all the sub-sets of the set A={a, b, c} can be given as { },{a},{b},{c}, {a,b},{a,c},{b,c}, {a,b,c}.

The number of sub-sets of a given set can be given by the formula 2^[n(S)] where [n(S)] is the number of elements in the set. If there are three elements, the number of sub-sets is 2^3 which is 8 sub-sets in all.