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.

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- Sep 9th 2007, 12:41 PMclockinglySet 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. - Sep 9th 2007, 12:46 PMPlato
Suppose A, B, and C are events. Express the following events in A, B, and C.

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

b) A and B occur, but C does not. $\displaystyle A \cap B \cap C\,'$ - Sep 9th 2007, 12:53 PMclockingly
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? - Sep 9th 2007, 12:57 PMPlato
- Sep 9th 2007, 01:03 PMclockingly
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?). - Sep 9th 2007, 01:16 PMJhevon
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: $\displaystyle (A \cap B' \cap C') \cup (A' \cap B \cap C') \cup (A' \cap B' \cap C)$

Quote:

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

- Sep 9th 2007, 02:38 PMclockingly
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') ? - Sep 9th 2007, 02:45 PMJhevon