SOLUTION: S = (N v H) / S v ~N // S ⊃ H This argument is: a. Invalid; fails in 1st line. b. Invalid; fails in 2nd line. c. Invalid; fails in 5th line. d. Invali

Algebra ->  Conjunction -> SOLUTION: S = (N v H) / S v ~N // S ⊃ H This argument is: a. Invalid; fails in 1st line. b. Invalid; fails in 2nd line. c. Invalid; fails in 5th line. d. Invali      Log On


   

Question 873855: S = (N v H) / S v ~N // S ⊃ H
This argument is:
a. Invalid; fails in 1st line.
b. Invalid; fails in 2nd line.
c. Invalid; fails in 5th line.
d. Invalid; fails in 4th line.
e. Valid
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
An argument is only invalid when you have all true premises and a false conclusion.

Make a truth table to get

S
 N H ~N N v H S = (N v H) S v ~N S -> H
T T T F T T T T
T T F F T T T F
T F T T T T T T
T F F T F F T F
F T T F T F F T
F T F F T F F T
F F T T T F T T
F F F T F T T T

and in line 2, there are all true premises, but a false conclusion.

This means we have an invalid argument and it looks like the argument fails on line 2 (of the truth table).