Given the argument: Q ∨ ∼ S / ∼(N • A) / S ∨ A / (P • N) ∨ (G • Q) // P • G
This argument is:
A) Valid.
B) Uncogent.
C) Invalid.
D) Cogent.
E) Sound.

Question

Quizplus · Accepted Answer

This argument is invalid, meaning that the conclusion does not necessarily follow from the premises. To determine validity, we can use a truth table:

P | N | A | G | S | Q | ~S | Q v ~S | N • A | ~(N • A) | S v A | P • N | G • Q | (P • N) v (G • Q) | P • G
T | T | T | T | T | T |  F |     T    |   T     |     F      |   T   |    T   |    T    |           T             |   T
T | T | T | T | T | F |  F |     T    |   T     |     F      |   T   |    T   |    F    |           F             |   F
T | T | T | T | F | T |  T |     T    |   T     |     F      |   T   |    T   |    T    |           T             |   T
T | T | T | T | F | F |  T |     T    |   T     |     F      |   F   |    F   |    F    |           F             |   F
T | T | T | F | T | T |  F |     T    |   T     |     F      |   T   |    T   |    T    |           T             |   T
T | T | T | F | T | F |  F |     F    |   F     |     T      |   T   |    T   |    F    |           F             |   F
T | T | T | F | F | T |  T |     T    |   T     |     F      |   T   |    T   |    T    |           T             |   F
T | T | T | F | F | F |  T |     T    |   T     |     F      |   F   |    F   |    F    |           F             |   F
T | T | F | T | T | T |  F |     T    |   F     |     T      |   T   |    T   |    T    |           T             |   F
T | T | F | T | T | F |  F |     T    |   F     |     T      |   T   |    T   |    F    |           F             |   F
T | T | F | T | F | T |  T |     T    |   F     |     T      |   T   |    T   |    T    |           F             |   F
T | T | F | T | F | F |  T |     T    |   F     |     T      |   T   |    T   |    F    |           F             |   F
T | T | F | F | T | T |  F |     T    |   F     |     T      |   T   |    T   |    T    |           F             |   F
T | T | F | F | T | F |  F |     T    |   F     |     T      |   T   |    T   |    F    |           F             |   F
T | T | F | F | F | T |  T |     T    |   F     |     T      |   F   |    T   |    T    |           F             |   F
T | T | F | F | F | F |  T |     T    |   F     |     T      |   F   |    T   |    F    |           F             |   F
F | T | T | T | T | T |  F |     T    |   T     |     F      |   T   |    T   |    T    |           F             |   F
F | T | T | T | T | F |  F |     T    |   T     |     F      |   T   |    T   |    F    |           F             |   F
F | T | T | T | F | T |  T |     T    |   T     |     F      |   T   |    T   |    T    |           F             |   F
F | T | T | T | F | F |  T |     T    |   T     |     F      |   T   |    T   |    F    |           F             |   F
F | T | T | F | T | T |  F |     T    |   T     |     F      |   T   |    T   |    T    |           F             |   F
F | T | T | F | T | F |  F |     T    |   T     |     F      |   T   |    T   |    F    |           F             |   F
F | T | T | F | F | T |  T |     T    |   T     |     F      |   T   |    T   |    T    |           F             |   F
F | T | T | F | F | F |  T |     T    |   T     |     F      |   T   |    T   |    F    |           F             |   F
F | T | F | T | T | T |  F |     T    |   F     |     T      |   T   |    T   |    T    |           F             |   F
F | T | F | T | T | F |  F |     T    |   F     |     T      |   T   |    T   |    F    |           F             |   F
F | T | F | T | F | T |  T |     T    |   F     |     T      |   T   |    T   |    T    |           F             |   F
F | T | F | T | F | F |  T |     T    |   F     |     T      |   T   |    T   |    F    |           F             |   F
F | T | F | F | T | T |  F |     T    |   F     |     T      |   T   |    T   |    T    |           F             |   F
F | T | F | F | T | F |  F |     T    |   F     |     T      |   T   |    T   |    F    |           F             |   F
F | T | F | F | F | T |  T |     T    |   F     |     T      |   F   |    T   |    T    |           F             |   F
F | T | F | F | F | F |  T |     T    |   F     |     T      |   F   |    T   |    F    |           F             |   F

As we can see, there are rows where the premises are true but the conclusion is false (namely, row 2 and row 6). Therefore, the argument is invalid.

Given the Argument: Q ∨ ∼ S / ∼(N •