Question

Can someone help me? I drew a venn diagram and put 4 in the middle and 2 in the overlapping sections but I don't know what to put in the singles… A,B and C?

A universal set U consists of 12 elements. If sets A, B, and C are proper subsets of U and n(U)=12, n(A∩B)=n(A∩C)=n(B∩C)=6, n(A∩B∩C)=4, and n(AUBUC)=10, Determine
a) n(AUB)
b) n(A'UC)
c) n(A∩B)'

Answer 1

Draw a Venn diagram of three overlapping circles with a box round them for the universal set. Make sure that there is a triple overlap in the middle.

n(A n B n C) = 4 tells you that there are 4 in the middle triple overlap.

n(A n B) = 6 tells you that there are 6 in the A and B overlap. 4 if these are already in the middle so put 2 in the A, B overlap that is not part of the middle. Do the same for the other pairs.

n(A U B U C) = 10 tells you that the three sets together contain 10 elements. How many does that leave for the single parts? How many does it leave outside of them all?

You should now be able to answer the questions at the end.