In a school that has

20

teachers,

10

teach Mathematics,

8

teach Social Studies, and

6

teach Science. Two teach both Mathematics and Social Studies, but none teach both Social Studies and Science. How many teach both Mathematics and Science?

Answer: 2

In this school the number of teachers would be:

Mathematics (M) = 10

Social Studies (SS) = 8

Science (S) = 6

Total teacher = 20

Two teach both Mathematics and Social Studies

M∩SS = 2

none teach both Social Studies and Science

SS∩S = 0

Using the calculation for the total teacher you can determine M∩S:

Total teacher = M + SS + S - M∩SS - M∩S - SS∩S

Total teacher = M + SS + S - M∩SS - M∩S - SS∩S

20 = 10+8+6 - 2 - M∩S - 0

20 = 22 - M∩S

M∩S = 22=20 = 2