Sets

6. Proper Subsets

Since every set A is a subset of itself, we call B a proper subset of A if, first, is a subset of A and secondly, if B is not equal to A. More briefly, B is a proper subset of A if:

B⊂A and B≠A

In some books “B is a subset of A” is denoted by

B⊆A

and B” is a proper subset of A” is denoted by

B⊂A

We will continue to use the previous notation in which we do not distinguished between a subset and a proper subset.