Question 1164833: Given the following logical expression, place the operations in the order in which you would apply, from first operation to last.
p → q ∨ ~r
Answer by CPhill(2189)   (Show Source):
You can put this solution on YOUR website! To determine the correct order of operations for the logical expression , we follow the standard rules of **operator precedence** in propositional logic.
The general hierarchy of operations is:
1. **Parentheses** (None in this expression)
2. **Negation** ( or )
3. **Conjunction** () and **Disjunction** ()
4. **Conditional** ()
5. **Biconditional** ()
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### Order of Application
Based on these rules, here is the order in which you would apply the operations for this expression:
1. **First Operation: Negation ()**
You must first find the truth value of "not " before it can be used in any other operation.
2. **Second Operation: Disjunction ()**
Following the hierarchy, the "OR" () operator is applied next. You take the result of and combine it with .
3. **Last Operation: Conditional ()**
The arrow (if-then) is the "main operator" here. It is applied last, using as the antecedent and the entire result of the previous step as the consequent.
### Summary Table
| Step | Operation | Name | Resulting Sub-expression |
| --- | --- | --- | --- |
| 1 | | Negation | |
| 2 | | Disjunction | |
| 3 | | Conditional | |
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Would you like me to construct a **truth table** for this expression to see how these operations interact?
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