# Statistics with Probability

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• #12808

Given a set of events (B) is equivalent to the sample set less another set of events (A), can one simply express set B as S – A? Is there a more formal way of expressing that?

#15557

Nevermind, I found the answer.

But, for anyone curious, B would be expressed as the complement of A (A^c).

#15565

I am glad that your were able to find the standard designation (complement). However, you stumbled across an important generalization of complement which is set difference. Given two sets A and B, A – B or A B are all elements in A that are not in B. The complement A^c is then the set difference between the universal set (the sample space S) and A or
A^c = S A

By the way, I edit here your question so that it uses the terminology of probability correctly: An event B is equivalent to the sample space less another event A, can one simply express set B as S – A? Is there a more formal way of expressing that?

Remember that an event is a set or collection of outcomes. So do not in general say “set of events”.

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