Negation can be viewed as an operator that takes a proposition and returns a proposition. Similarly, conjunction, disjunction, conditional, and biconditional can be viewed as binary operators that take two propositions and returns a proposition. Similarily to the precedence of operations for arithmetic operators, there is a prescribed order of precedence for the logical operators. It is given in Figure 1.1.5.1.
For example, the precedence order means that \(\lnot p\land q\) means the same thing as \((\lnot p)\land q\) . Omitting the parentheses in this case is standard and acceptable. We will allow this.
The precedence also means that \(p\land q\lor r\) means \((p\land q)\lor r\) . The omission of parentheses in this case is confusing. We will not allow this in this course.
Another example that will not be allowed is the following. The precedence gives that \(p\land q \implies r\) means \((p\land q)
\implies r\) . In this case also, parentheses should be added for clarity.
