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

Question 1164609: 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(2264) (Show Source): You can put this solution on YOUR website!
Following the standard rules of **Logical Precedence**, we evaluate the operations from the most "tightly bound" operator to the "main connective."
The hierarchy is as follows:
1. **Negation** ($\sim$)
2. **Conjunction** ($\land$)
3. **Disjunction** ($\lor$)
4. **Conditional** ($\to$)
---
### **Order of Application**
For the expression **$\sim p \land q \to r$**, the operations should be applied in this order:
1. **First: Negation ($\sim p$)**
The "NOT" operator is applied only to the variable immediately following it. You must flip the truth value of $p$ first.
2. **Second: Conjunction ($\sim p \land q$)**
The "AND" operator takes precedence over the conditional. You evaluate the relationship between the result of Step 1 and $q$.
3. **Last: Conditional ($\dots \to r$)**
The "IF...THEN" operator is the main connective here. It evaluates the relationship between the entire left-hand side (the antecedent) and $r$ (the consequent).
### **Summary Table**
| Order | Operation | Symbol | Resulting Grouping |
| :--- | :--- | :--- | :--- |
| **1st** | Negation | $\sim$ | $(\sim p)$ |
| **2nd** | Conjunction | $\land$ | $(\sim p \land q)$ |
| **3rd** | Conditional | $\to$ | $((\sim p \land q) \to r)$ |
---
**Wait, why not the arrow first?**
In logic, the conditional ($\to$) is considered "weaker" than conjunction or negation. If you wanted the arrow to be evaluated first, the expression would have required parentheses like this: $\sim p \land (q \to r)$. Without them, we follow the hierarchy above.
Are you working on a truth table for this specific statement?
RELATED QUESTIONS
Given the following logical expression, place the operations in the order in which you... (answered by CPhill)

Given the following logical expression, place the operations in the order in which you... (answered by CPhill,Edwin McCravy)

a graph with the following points: (-6,0), (-3,3), (0,0), (1,-1), (3,-1). List the... (answered by Edwin McCravy)

Apply the Order of Operations to simplify the following expression: 2x[(5x2 � 3x + 2) �... (answered by Marth)

(x + 4)(x - 5) If you were to multiply the two factors in the expression which operation (answered by ewatrrr)

What operation should be perfermided first in this expression? 8 - 3 + 12 / 3 x 2... (answered by Alan3354,KMST)

Apply the order of operations to simplify the following expression.... (answered by Theo)

I need help with solving this problem of order of operations please 1. Apply the Order (answered by CubeyThePenguin)