Give an example of a subset and a proper subset. Explain the difference between a subset and proper subset.
http://sdp.mathforum.org/library/drmath/view/52426.html
Sure! Let's say we have a set A = {1, 2, 3}.
A subset is a set that contains some or all elements of another set. For example, if we consider the set B = {1, 2}, then B is a subset of A because all the elements of B (1 and 2) are also found in A. We can represent this as B ⊆ A.
On the other hand, a proper subset is a subset that contains some, but not all, elements of another set. If we consider the set C = {2, 3}, then C is a proper subset of A because it contains some elements of A (2 and 3), but not all of them. In other words, C ⊂ A.
To distinguish between the two, we use the symbols "⊆" for subset and "⊂" for proper subset.
So, in our example, we can say that B is a subset of A (B ⊆ A), and C is a proper subset of A (C ⊂ A).