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Probability 'compliment' identities? watch

1. Could someone clarify what i can do to simplify compliments in event probability?

I know for certain that:

Could i do anything similar with:

or

or

And also with the above 3 examples but using or instead of
2. Have you heard of De Morgan's Laws?
3. (Original post by GHOSH-5)
Have you heard of De Morgan's Laws?
I have actually, and now i remember, it does explain how to simplify when both events are compliments, but what when only one of the events in the bracket is a compliment? And how would this work for something like
P(E|F^c)?
4. (Original post by nugiboy)
I have actually, and now i remember, it does explain how to simplify when both events are compliments, but what when only one of the events in the bracket is a compliment? And how would this work for something like
P(E|F^c)?
If only one is a compliment, then for example, you can do the folllowing:

: Let . Hence by De Morgan's Laws: .

For , due to the previous paragraph.
5. Thanks! That pretty much makes sense.

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