In a survey of a TriDelt chapter with 50 members, 18 were taking mathematics, 37 were taking English, and 7 were taking both. How many were not taking either of these subjects?

Answer 1

draw 2 intersecting circles, label one M and the other E

place 7 in the intersection of both
Now look at the M circle, it should contain 18, but we have already placed 7 in that circle, so put 11 in the open part of circle M
Now look at the E circle, it should contain 37, but we have already placed 7 in that circle, so put 30 in the open part of circle E

now adding these numbers up I get
11 + 7 + 30 = 48

but we surveyed 50 people, so 2 must have been outside our two circles ----> 2 were not taking either of these.

As and equation we could have done:
Number(M or E) = number(M) + number(E) - number (M AND E)
number(M OR E) = 18+37 - 7 = 48

You will probably get questions with 3 circles.
Repeat the same method as above, except you would have an inner intersection of 3 items, start with that.