Convert each of the following arguments into formal statements e,g define sentences existentially and/or universally quantified statements. Then determine which rules of logic have been applied and explain whether or not they have been applied correctly. 1. If you do the homework you will pass the final. Somebody did not pass the final. Therefore somebody did not do the homework.
Convert each of the following arguments into formal statements e,g define sentences existentially and/or universally quantified statements. Then determine which rules of logic have been applied and explain whether or not they have been applied correctly.
1. If you do the homework you will pass the final. Somebody did not pass the final. Therefore somebody did not do the homework.
Answer:
First, break the argument into premises and a conclusion.
P1 = if you do the homework you will pass the final
P2 = Somebody did not pass the final
C = Somebody did not do the homework
Now assign letters to the above
P = You do the homework
Q = You will pass the final
R = Somebody passed the final
S = Somebody did the homework
P1 = (P->Q)
P2 = ~R
C = ~S
Thus the given argument will be converted into
(P->Q),(~R) |= (~S)
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