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Does the definition of "mutually exclusive" include the case where neither A nor B happen?

I ask this because I remember in logic, "xor" has to be A or B and doesn't include the case where neither A nor B happen.

Here is an example that might help explain what I want to ask.

A: seeing Superman

B: seeing Clark Kent

We can only see either Superman or Clark Kent at a time, and never see them both, and we see neither of them sometimes.

In this case, can we say A and B are mutually exclusive?

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    "A and B are mutually exclusive" means only that A and B can't happen at the same time. (But I think this question would be more appropriate at e.g. english.stackexchange.com, there isn't really a philosohpy aspect here.) Apr 29, 2021 at 17:30
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    Yes, it includes it. To exclude neither happening the term is "collectively exhaustive". See Wikipedia or dictionaries for these types of questions
    – Conifold
    Apr 29, 2021 at 17:41

2 Answers 2

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"Mutually exclusive" does not mean "A XOR B." It means "NOT (A AND B)" or equivalently "(NOT A) OR (NOT B)."

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"Mutually exclusive" means either one excludes the other and is synonymous with the concept of disjointness.
In logic terms, "A and B are mutually exclusive" should be written as (A IMPLIES (NOT B)) AND (B IMPLIES (NOT A)).
If we make a truth table for this, we see its truth value is TRUE when A = B = FALSE.

If in addition to being mutually exclusive A and B exhaust the possibilities for what can happen (e.g. a coin flip can come up either A = heads or B = tails), we often say that A and B "partition", or form a partition of, the set of possibilities. But this is a strictly stronger condition than mutual exclusivity, and is not implied by mere mutual exclusivity.

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