Please help with sets.

Question

Let A and B be subsets of a universal set U and suppose n(U)=210, n(A)=100, n(B)=60, and n(A∩B)=30. Compute n(Ac∩Bc).

 

 

 

 

80

150

100

90

180

200

 

Please help. Thank you 

Answer 1

Make two semi-overlapping circles, labeled (on their circumferences) A and B, respectively.From the given data, place 30 in the intersection of A & B.

The other part of A must be 70, to make the total of 100 in circle A (two parts combined).

The non-overlapping portion of circle B, similarly, must contain 30.

That 130 total so far, so the remainder, 80, is placed OUTSIDE both circles.

This is called a Venn diagram, and it's the way to go on such problems.

 

Now, what does n(Ac∩Bc) mean? If small c means same as ' (for "non") then it's asking for intersection of the outside of A with outside of B.  You should work that out by shading (to visualize), and see what area(s) that covers, and add up the numbers in the double-shaded area (different colors work best).