If there exists any priorities between logical operators. I do not mean in any specific programming language, but in the mathematics. For example, How can we interpret A<=>B<=>C ?
Thanks
If there exists any priorities between logical operators. I do not mean in any specific programming language, but in the mathematics. For example, How can we interpret A<=>B<=>C ?
Thanks
In everyday mathematical reasoning, the notation $A\Leftrightarrow B\Leftrightarrow C$ is overwhelmingly likely to mean that $A$, $B$, and $C$ are all equivalent -- that is, $(A\Leftrightarrow B)\land(B\Leftrightarrow C)$.
That usage is fairly rare in formal logic, but you wouldn't typically see $A\Leftrightarrow B\Leftrightarrow C$ written down in formal logic at all. Instead one writes $(A\Leftrightarrow B)\Leftrightarrow C$ or $A\Leftrightarrow(B\Leftrightarrow C)$ according to which of them one means.
One does see things like $A\Rightarrow B\Rightarrow C$ (with single implications) written down in formal logic, but there are competing conventions whether this means $(A\Rightarrow B)\Rightarrow C$ or $A\Rightarrow(B\Rightarrow C)$. The latter convention is very common among computer scientists, whereas mathematical logicians are somewhat more likely to use the former.
Again, in semi-formal everyday reasoning "$A\Rightarrow B\Rightarrow C$" is very commonly used simply as a shorthand for asserting $A\Rightarrow B$ and $B\Rightarrow C$ at the same time.