Lets say you have a set S = {1, 2, 3}

[IKonquer]

Lets say you have a set S = {1, 2, 3}

The subsets would be the following:
{} (nullset)
{1}, {2,}, {3}
{1, 2}, {2, 3}, {1, 3}
{1, 2, 3}

Would {1, 2} be considered the same subset as {2, 1}?

 

[zoek]

Lets say you have a set S = {1, 2, 3}

The subsets would be the following:
{} (nullset)
{1}, {2,}, {3}
{1, 2}, {2, 3}, {1, 3}
{1, 2, 3}

Would {1, 2} be considered the same subset as {2, 1}?

yes - the set {1, 2} is equal to {2, 1}.

 

[ArcanaNoir]

You can verify that they are the same set (prove is such a formal word...)
Since the power set of S is the set set of all subsets of S, and the power set has 2^n elements, (n being the number of elements in S), you know you should have 8 subsets in this example. If {1,2} is a different set than {2,1}, you'd have more sets than allowed, so they must be the same.