SOLUTION: Given the following logical expression, place the operations in the order in which you would apply, from first operation to last. p → q ∨ ~r

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Question 1164610: Given the following logical expression, place the operations in the order in which you would apply, from first operation to last.
p → q ∨ ~r

Found 2 solutions by CPhill, Edwin McCravy:
Answer by CPhill(2264)   (Show Source): You can put this solution on YOUR website!
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** ($\leftrightarrow$)
---
### **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?
Answer by Edwin McCravy(20086)   (Show Source): You can put this solution on YOUR website!
Remember the sentence "Never Argue Over Ideas" for N, A, O, I. 

NOT, AND, OR, IF-THEN

p → q ∨ ~r

The proposition is 

p IF THEN q OR NOT r

NOT comes first, so put parentheses around ~r

p → q ∨ (~r)

AND comes second.  There are no ANDs, so copy it over.

p → q ∨ (~r)

OR comes third. There is one OR, so put brackets around q ∨ (~r) 

p → [q ∨ (~r)]

[You could think of the girl's name "NAOMI" but you would have to remember to
ignore the M.]

Edwin
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