SOLUTION: The freshman class at a college has a total of 250 students. One hundred and ten freshmen take math and 200 take English, while 75 take neither. How many freshman take both math an

You have an universal set of 250 elements and two its subsets, M (=Math) of 110 elements and E (=English) of 200 elements.


The union of the subsets M and E contains 250-75 = 175 elements.


Now use the formula


    n(M U E) = n(M) + n(E) - n(M n E)


for the numbers of elements.


From this formula,


    n(M n E) = n(M) + n(E) - n(M U E) = 110 + 200 - 175 = 135.


Answer.  135 freshman take both Math and English.