What is the difference between ⊆ and ⊂ ?
I am currently using Probability and Statistics: Crash Course. It told what ∪ and ∩ meant, but not ⊂. Strange. I gather that the latter means "subset of", but I don't know what ⊆ means at all.
It says that Theorem 1-1 is:
"If A1 ⊂ A2, then
P(A1) <= P(A2) and P(A2-A1) = P(A1) - P(A2)"
The above is as written, double-checked (except that the numbers are in subscript, and <= is a single character).
The first part sounds right, but what about the second part? If A1 is a subset of A2, then shouldn't P(A1) - P(A2) be a negative number?
And what is with subtracting A1 from A2 in parenthesis? I didn't think events necessarily had mathematical values, though probabilities of events obviously do.