80 students were asked if they like math, science or humanities. 24 students did not like either of the subjects, 9 liked math only, 16 liked science only, 9 liked humanities only, 12 liked math and humanities, 7 liked math and science and 9 liked humanities and science.
a) How many students like all three subjects?
b) How many students like math or science?
c) How many students don't like humanities?
Here's a venn diagram displaying the given information:
a) finding the intersection of sets M, S and H
-2 |M∩S∩H|= (80 - 24) - (9 + 16 + 9) - (12 + 7 + 9)
-2 |M∩S∩H|= 56 - 34 - 28
-2 |M∩S∩H|= 22 - 28
-2 |M∩S∩H|= -6
I can't do b) or c) because when I say the intersection is 3, then all the other numbers in the venn diagram change (obviously). For example, if the intersection is 3, then the number of people who like math and science = 4 (7 - 3) and the number of people who like math and humanities = 9 (12 - 3). But when I add up the newfound numbers (3 + 9 + 4), I get 16 and I can't do 9 - 16 (which is -5, A NEGATIVE NUMBER!!!) Could someone please let me know what I have done wrong and how the heck I'm supposed to figure out the intersection of three sets?! Any help would be greatly appreciated.