Symbol for Mutual Inclusive events

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is there any symbol for mutual inclusive(opposite of Mutually exclusive) events in probability.

I meant to say is for OR we have U symbol in Set Theory. Likewise is there any symbol for Mutual Inclusiveness.

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1 Answer

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You want to say that two events $A$ and $B$ satisfy

1. If $A$, then $B$;
2. If $B$, then $A$.

That is, $A$ if and only if $B$. Thus $A$ and $B$ are mutually inclusive if and only if $A$ and $B$ happen simultaneously. We might say that $A$ and $B$ are equivaent events, or that $A$ and $B$ are concurrent events. (I don't think either notation is standard.)

Symbolically, I suppose you'd want to use $A \equiv B$ or $A=B$ (denoting the fact that mutual inclusion is an equivalence relation). I don't think any particular form is standard.

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