SOLUTION: Use direct or indirect truth table method to determine whether the following argument is valid.
S ≡ (N • H) / S v ~N // S ⊃ H
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Question 1199150: Use direct or indirect truth table method to determine whether the following argument is valid.
S ≡ (N • H) / S v ~N // S ⊃ H
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!
I'll use the ampersand symbol & in place of the dot.
So instead of N • H, I'll write N & H.
I'll use an arrow in place of the horseshoe symbol.
Refer to this list of truth table rules
https://www.algebra.com/algebra/homework/Conjunction/truth-table1.lesson
For example, the first rule mentioned in that link will help us determine the column labeled N & H.
Here is the truth table for the current logical argument
| | | | Premise | | Premise | Conclusion |
| S | N | H | N & H | S = (N & H) | ~N | S v ~N | S --> H |
| T | T | T | T | T | F | T | T |
| T | T | F | F | F | F | F | F |
| T | F | T | F | F | T | T | T |
| T | F | F | F | F | T | T | F |
| F | T | T | T | F | F | F | T |
| F | T | F | F | T | F | T | T |
| F | F | T | F | T | T | T | T |
| F | F | F | F | T | T | T | T |
Circle the rows that have a false conclusion.
This would be row 2 and row 4.
Now look through the premises for row 2. Ask yourself: "are all of the premises true for this row?" The answer is "no". Both premises are false here.
In row 4, the first premise is false while the second premise is true. Therefore we don't have all true premises here either.
Since we do not have a list of all true premises lead to a false conclusion, we can definitively say this argument is valid.
An invalid argument is where all true premises lead to a false conclusion.
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