Question 1164610
To determine the correct order of operations for the logical expression $p \to q \lor \neg r$, we follow the standard **Order of Logical Precedence**. Much like "PEMDAS" in algebra, logic has a hierarchy that dictates which operator is evaluated first.

The standard order is:
1.  **Negation** ($\neg$ or $\sim$)
2.  **Conjunction** ($\land$)
3.  **Disjunction** ($\lor$)
4.  **Conditional** ($\to$)
5.  **Biconditional** ($\leftrightarrow$)

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### **Order of Application**

Based on the rules above, here is the step-by-step order for your expression:

1.  **First: Negation ($\sim r$)**
    The "NOT" operator has the highest priority. You must determine the truth value of $\sim r$ before it can be used in any other operation.
2.  **Second: Disjunction ($q \lor \sim r$)**
    The "OR" operator is next in the hierarchy. You take the result from the first step and evaluate it against $q$.
3.  **Last: Conditional ($p \to \dots$)**
    The "IF...THEN" operator has the lowest priority in this expression. It acts as the "main connective," linking $p$ to the result of the entire right-hand side.

### **Summary Table**
| Order | Operation | Symbol |
| :--- | :--- | :--- |
| 1st | Negation | $\sim$ |
| 2nd | Disjunction | $\lor$ |
| 3rd | Conditional | $\to$ |

**Visual Grouping:** If you were to add parentheses to show this order, the expression would look like this: $(p \to (q \lor (\sim r)))$.

Are you building a truth table for this expression, or just practicing the syntax?