SOLUTION: Topics In Contemporary Math Arguments Use truth tables to determine if each of the following arguments are valid or invalid. 2) If you are superstitious, then do not walk

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Question 1190253: Topics In Contemporary Math
Arguments
Use truth tables to determine if each of the following arguments are valid or invalid.
2) If you are superstitious, then do not walk under a ladder.
If you do not walk under a ladder, then you are superstitious.
Therefore, you are superstitious and you do not walk under a ladder.

Found 2 solutions by Solver92311, math_tutor2020:
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!

S = "You are superstitious"

W = "You walk under a ladder"

~W = "You do not walk under a ladder" 


  S   W   ~W   S & ~W

  T   T    F     F
  T   F    T     T
  F   T    F     F
  F   F    T     F

S & ~W could be true or false.  S -> ~W and ~W -> S are both irrelevant to the conclusion.

The argument is invalid

John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

S = you are superstitious
W = you walk under a ladder
~S = you are not superstitious
~W = you do not walk under a ladder

Premise 1: S -> ~W
Premise 2: ~W -> S
Conclusion: S & ~W

Truth table:
Premise 1Premise 2Conclusion
SW~S~WS -> ~W~W -> ~SS & ~W
TTFFFTF
TFFTTTT
FTTFTTF
FFTTTFF
Notes:
  • P -> Q is false when P is false and Q is true, otherwise it's true.
  • P & Q is true when both P and Q are true together, otherwise it's false
  • Whatever you find in column S, flip it to get ~S, and vice versa. Same goes for W to ~W as well.
In the table above, the row marked in red highlights a case when we have all true premises but they lead to a false conclusion.

This directly leads to the fact the argument is invalid.