There is a logical or mathematical symbol for compatibility/incompatibility? Exists a symbol in logic or mathematics to relate two or more compatibility or incompatibility conditions? I dont want to specify a determined area of study (topology, algebra, etc...) I just want to know about this topic in a broad sense, if it exists something like this and the related area. This is just for curiosity, sorry if my question is so undefined or broad but I dont have any clue about this.

The Sheffer stroke, introduced in 1913 and written $\mid$, is often described as asserting that two propositions are incompatible. (For example, Whitehead and Russell describe it this way.) The assertion $$A\mid B$$ means precisely that $A$ and $B$ cannot both be true.