Construct a complete truth table for each of the following arguments. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
-M ⊃ (N • ∼O)
N ⊃ (O $ \lor $ M) / O ⊃ ∼N
A) Valid
B) Invalid. Counterexample when M, N, and O is true
C) Invalid. Counterexample when M and N are true and O is false
D) Invalid. Counterexample when M is false and N and O are true
E) Invalid. Counterexample when M and N are false and O is true

Question

Quizplus · Accepted Answer

The truth table for the argument is as follows:

| M | N | O | M ⊃ (N • ∼O) | N ⊃ (O $ \lor $ M) | O ⊃ ∼N |
|---|---|---|----------------|----------------|----------------|
| T | T | T | F | T | F |
| T | T | F | F | F | T |
| T | F | T | F | T | F |
| T | F | F | F | T | T |
| F | T | T | T | T | F |
| F | T | F | T | F | T |
| F | F | T | T | T | F |
| F | F | F | T | T | T |

The argument is invalid because there is a row where all the premises are true but the conclusion is false. This happens in row 4, where M is false, N is true, and O is true. In this case, the first premise is true (because the antecedent is false), and the second premise is true because N is true and O or M is also true. However, the conclusion is false because O is true and N is also true, so ∼N is false. Therefore, the argument is invalid and the best choice is D.

Construct a Complete Truth Table for Each of the Following ∨ \lor ∨

Construct a Complete Truth Table for Each of the Following $\lor$