In bivariate probability: How do I denote different cases at the same time?

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I have two random variables $X$ and $Y$, each of which can take on the values $1$ or $0$. I was browsing other questions for examples of notation, but couldn't find any. In particular I want to know how I can write down

$P(X=1,Y=0)+P(X=0,Y=1)+P(X=1,Y=1)$

more concisely, besides $1-P(X=0,Y=0)$?