# Math Help - Set theory question

1. ## Set theory question

The following question was confusing me, so if anyone could help it would be greatly appreciated!

Suppose A, B, and C are events. Express the following events in A, B, and C.

a) Only A occurs
b) A and B occur, but C does not.

2. Suppose A, B, and C are events. Express the following events in A, B, and C.

a) Only A occurs $A \cap B\,' \cap C\,'$

b) A and B occur, but C does not. $A \cap B \cap C\,'$

3. Thanks! So if I wanted to express the fact that all three events occur, I'd just do

A intersect B intersect C?

And if I wanted to express the fact that none of the three events occurs, I'd just do

A' intersect B' intersect C?

4. Originally Posted by clockingly
Thanks! So if I wanted to express the fact that all three events occur, I'd just do
A intersect B intersect C?
And if I wanted to express the fact that none of the three events occurs, I'd just do
A' intersect B' intersect C?
Yes, with C' for the last one.

5. Thanks! Sorry, one last question - how would I express the fact that exactly one of the three events occurs?

Or the fact that at most one of the events occurs?

I guess I'm confused about this because in each of these cases, it's not set in stone the specific events that occur (A, B, C?).

6. Originally Posted by clockingly
Thanks! Sorry, one last question - how would I express the fact that exactly one of the three events occurs?
use the union.

if exactly one occurs, then that one could be A or it could be B or it could be C.

so we have: $(A \cap B' \cap C') \cup (A' \cap B \cap C') \cup (A' \cap B' \cap C)$

Or the fact that at most one of the events occurs?
This means one or less occur. Take what i did above as an example and try to figure this one out

7. Thanks!

So if at the most one of the events occurs, you would have:

(A intersect B' intersect C') U (A' intersect B intersect C') U (A' intersect B' intersect C') U (A' intersect B' intersect C') ?

8. Originally Posted by clockingly
Thanks!

So if at the most one of the events occurs, you would have:

(A intersect B' intersect C') U (A' intersect B intersect C') U (A' intersect B' intersect C') U (A' intersect B' intersect C') ?
the third set of brackets should have C not C'