Question 1064329
Number taking S=30
Number taking A=40
There has to be overlap, or there would be 70 students.  There are only 45
Number taking both = at least 25, the minimum.
When you have  p(A)+p(B), and there is no overlap, the probability of OR is their sum. The probability of AND is 0, because there is no overlap.  If there is overlap, you are double counting them, so the probability of both (AND) has to be accounted for. 
Here, there can't be more than 45 students.  It is possible 30 are taking both.  It can't be more, or the number taking Spanish would be higher.  It could also be 29...25.  It can't be lower than 25, otherwise when we subtract the double counting, we would end up with more students than we started.