SOLUTION: Topics In Contemporary Math Arguments Use truth tables to determine if each of the following arguments are valid or invalid. 1) Ted will get a Big Mac or a Whopper with c

Question 1190252: Topics In Contemporary Math
Arguments
Use truth tables to determine if each of the following arguments are valid or invalid.
1) Ted will get a Big Mac or a Whopper with cheese.
Ted did not get a Whopper with cheese.
Therefore, Ted got a Big Mac.

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

This is a proof of the Disjunctive Syllogism

B = Ted will get a Big Mac

W = Ted will get a Whopper with cheese

B W ~W B v W ~W & (B v W) ~W & (B v W) -> B T T F T F T T F T T T T F T F T F T F F T F F T

Last column: A conditional is false ONLY if the antecedent is true and the consequent is nevertheless false. Since B is true in the only case where not W and B or W is true, all of the cases are true in the last column.

John

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

From
I > Ø

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

B = Ted will get a Big Mac
W = Ted will get a Whopper with cheese
~W = Ted will not get a Whopper with cheese

Premise 1: B v W
Premise 2: ~W
Conclusion: B

Truth Table

Premise 1 Premise 2 Conclusion
B W B v W ~W B
T T T F T
T F T T T
F T T F F
F F F T F

Notes:
B v W is only false when both B and W are false; otherwise, its true.
The first and last column are identical copies of each other
The ~W column is the flipped version of the W column
Now look through the table and see if there are any situations where we have all true premises which lead to a false conclusion. No such thing happens.
Row two has all true premises, and those true premises lead to a true conclusion.
We ignore any rows with at least one false premise.

Since we couldn't find any rows that had all true premises leading to a false conclusion, this means that the argument is valid

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