Question

How can you find the formula for the union of set A, B, C, D if A and B are mutually exclusive?

(This is NOT homework)

Answer 1

Are you talking about the size of the union?

Answer 2

I want to find AUBUCUD assuming that A and B have no intersections.

Answer 3

You can use the inclusion-exclusion principle.

Answer 4

That works only if all of the sets have intersections with each other.
In this case, A and B have no intersection, so the inclusion-exclusion principle doesn't apply here.

Answer 5

The intersection of mutually exclusive sets is the empty set. The inclusion-exclusion principle holds.

Answer 6

i.e., for sets A and B that are mutually exclusive, |AUB| = |A| + |B| - |A intersect B|

|A intersect B| is the empty set, so |AUB| = |A| + |B|.

Answer 7

Wait...
I got it!

Answer 8

I had a brain cramp...

Answer 9

Glad to hear! I hope I helped in some way.

Answer 10

Thank you for reminding me the inclusion-exclusion principal

Answer 11

Can't believe i forgot that

Answer 12

No problem! I liked seeing a set theory question on here--most of them are boring algebra and geometry

Answer 13

agree