2.3 Precedence of operators

When you see an expression, you must be able to recognise what is it. For instance, $A\vee B\Rightarrow C$ is an implication (not a disjunction!), because $\Rightarrow$ is evaluated last (it has lower priority than $\vee$).

Here there are the operators, inversely sorted by priority:

• $\Longleftrightarrow$
• $\Rightarrow$
• $\vee$ and $\wedge$ (they have the same priority)
• $\neg$

This means that $\neg$ is the one that most ``sticks'' to the symbol it has next. See this example about when and where are needed the parenthesis:

$P\vee\neg Q\Rightarrow R\wedge P\Longleftrightarrow\neg(R\vee S)\wedge A\Rightarrow B$ is the same as $(\ (P\vee(\neg Q))\ \Rightarrow\ (R\wedge P)\ )\Longleftrightarrow(\ ((\neg(R\vee S))\wedge A)\Rightarrow B\ )$

But don't panic, I won't use again expressions that long.