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Proper Subset

Let A and B be two sets. We say that A is a proper subset of B if A is a subset of B and A B. That is, A is a proper subset of B if A B and A B.
In some books, "A is a subset of B" is denoted by A  B
and "A is a proper subset of B" is denoted by A B.
In our lesson we shall use for both subset and proper subset.

Let A = {p, q, r, s, t} and B = {q, t}.

In the above, B is a proper subset of A since B is a subset of A and B A. 

We can also denote as B A.

In this problem Y is a proper subset of X and we can also denote as Y ⊂ X.




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