Question 996678: I'm having a really hard time with the following proof:
A&B, AvC :. (A->B) & (C->A)
My prof has warned us that the second premise, AvC, is a distraction, but I don't really understand how to do this then.
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
1. A&B
2. AvC
:. (A->B) & (C->A)
Your prof is wrong. This argument is not valid.
Here is the counter-example:
Suppose that A is false, B is true, and C is false.
Then A&B is false, AvC is false, therefore the
conjunction of the premises (A&B)&(AvC) is false.
Now let's look at the conclusion:
A->B is true, C->A is true, therefore (A->B) & (C->A) is true.
So this is a case where the conjunction of premises is false
and the conclusion is true.
So the argument is invalid. Be sure to tell your prof why.
Edwin
Answer by AnlytcPhil(1806)  (Show Source):
You can put this solution on YOUR website!
1. A&B
2. AvC
:. (A->B) & (C->A)
Your prof is wrong. This argument is not valid.
Here is the counter-example:
Suppose that A is false, B is true, and C is false.
Then A&B is false, AvC is false, therefore the
conjunction of the premises (A&B)&(AvC) is false.
Now let's look at the conclusion:
A->B is true, C->A is true, therefore (A->B) & (C->A) is true.
So this is a case where the conjunction of premises is false
and the conclusion is true.
So the argument is invalid. Be sure to tell your prof why.
Edwin
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