# Set theory question

• September 9th 2007, 12:41 PM
clockingly
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.
• September 9th 2007, 12:46 PM
Plato
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. $A \cap B \cap C\,'$
• September 9th 2007, 12:53 PM
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?
• September 9th 2007, 12:57 PM
Plato
Quote:

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.
• September 9th 2007, 01:03 PM
clockingly
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?).
• September 9th 2007, 01:16 PM
Jhevon
Quote:

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: $(A \cap B' \cap C') \cup (A' \cap B \cap C') \cup (A' \cap B' \cap C)$

Quote:

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
• September 9th 2007, 02:38 PM
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') ?
• September 9th 2007, 02:45 PM
Jhevon
Quote:

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'