What is the truth table for p v ( q arrow going straight across p )
To determine the truth table for the expression "p v (q → p)," we need to consider all possible combinations of truth values for the variables p and q.
Step 1: Identify the variables involved.
- p: a variable that can take on the truth values 'True' or 'False'.
- q: another variable that can also take on the truth values 'True' or 'False'.
Step 2: Determine all possible combinations of truth values for p and q.
- There are four possible combinations since each variable can have two distinct truth values:
- Combination 1: p = True, q = True
- Combination 2: p = True, q = False
- Combination 3: p = False, q = True
- Combination 4: p = False, q = False
Step 3: Evaluate the given expression for each combination of truth values.
- For each combination of truth values, we substitute the values of p and q into the expression "p v (q → p)" and determine the resulting truth value.
Let's build the truth table:
| p | q | q → p | p v (q → p) |
|-------|-------|-------|------------|
| True | True | True | True |
| True | False | True | True |
| False | True | False | False |
| False | False | True | True |
In this truth table, we evaluated the expression "p v (q → p)" for all possible combinations of truth values for the variables p and q. The resulting truth values are listed under the column labeled "p v (q → p)."