# Please give an example of a subset & a proper subset, explain the difference between a subset & proper subset.As we know, a set is just a collection of objects that are similar in some...

Please give an example of a subset & a proper subset, explain the difference between a subset & proper subset.

As we know, a set is just a collection of objects that are similar in some way, like a gaggle of geese, pride of lions, or an army of ants.

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### 1 Answer

Let us consider sets A and B. If every element of set A is an element of set B, we say that A is a subset of B.

For example if A is {1, 2, 3, 4, 5} and B is {1, 2, 3, 4, 5} then we can say A is a subset of B as all the elements of set A are also elements of set B. Two sets which have the same elements are subsets of each other. But A is not a proper subset of B in this case.

For a set A to be a proper subset of another set B, all the elements of A should be elements of B but A and B should not be equal. Or in other words, A should be a subset of B but B should not be a subset of A.

For example if A is {1, 2, 3, 4} and B is {1, 2, 3, 4, 5} then A is a proper subset of B. Here we see that all the elements of A are elements of B but all elements of B are not elements of A. A is a subset of B but it is not equal to B.