Exercise: PL parentheses
Given that,
- \(\neg\) binds most tightly,
- \(\land\) and \(\lor\) bind more tightly than \(\rightarrow\), and their binding power is the same,
- Outermost parentheses are eliminable,
- \(\land\) and \(\lor\) are both associative.
Restore the full parentheses in the following formulas:
- \[\neg p \lor q \rightarrow r\]
- \[p \rightarrow q \land r\]
- \[p \land q \land r\]
- \[p \land q \lor r\]
- \[p \rightarrow q \rightarrow p\]
Eliminate the parentheses as much as possible in the following formulas:
- \[(p\rightarrow q) \lor r\]
- \[(p \lor (q \lor r)) \rightarrow (p \land \neg (r \lor q))\]
- \[((p \land q) \lor r)\]
- \[\neg (p \lor r \lor q)\]
- \[((p \land q) \lor r) \lor p))\]