Solving Complementary Sets: n(A U B)

[blunted]

Homework Statement

If n(A - B) = 5, n(A' - B) = 4, n(A') = 10, n(B'-A') = 12. What is n(AUB) = ?

Homework Equations

The Attempt at a Solution

I drew a big rectangle and inside 2 intersected diagrams A and B. I drew 5 dots in the (( of diagram A. Now that A' is complementary that means they have nothing in common, so I drew 5 dots outside of the diagrams(inside the rectangle).
n(B' - A') = 12. If A' = 10. B' = 2?

About the question above. NOTHING else is given, just that.

 

[jedishrfu]

so start with the venn diagram and put in the numbers you know and for (A intersection B) put in an X and try to use your logic to figure out the counts for the four areas and then the A union B should be obvious.

 

[Mark44]

Homework Statement

If n(A - B) = 5, n(A' - B) = 4, n(A') = 10, n(B'-A') = 12. What is n(AUB) = ?

Homework Equations

The Attempt at a Solution

I drew a big rectangle and inside 2 intersected diagrams A and B.

You're assuming that the two sets intersect, which might not be true, based on the given information.

I think there are four possibilities:
1) A and B are disjoint (no common members)
2) A and B intersect for some members, but not all of them (i.e., some members of A aren't also in B, and vice versa)
3) A is completely contained in B
4) B is completely contained in A

Draw a Venn diagram for each of these scenarios. For each one identify the sets A - B, A' - B, A', and B' - A'. See if you can sprinkle your dots so that the four given conditions are met. You should then be able to determine n(A U B).

I drew 5 dots in the (( of diagram A. Now that A' is complementary that means they have nothing in common, so I drew 5 dots outside of the diagrams(inside the rectangle).
n(B' - A') = 12. If A' = 10. B' = 2?

About the question above. NOTHING else is given, just that.