SOLUTION: There is only one premise, and the conclusion has different letters Here it is: A -> B We have to show (A & C) -> B

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Question 251007: There is only one premise, and the conclusion has different letters
Here it is:
A -> B
We have to show (A & C) -> B
Found 2 solutions by richwmiller, jim_thompson5910:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
A->B
(A&C)->B
There are two problems with this.
& is not a mathematical symbol such as + and * for addition and multiplication
SO I do not know what you mean by A & C
Let's say that & means addition
If C is negative
A-C is not necessarily = nor greater B
9-> 4
9-7 is not greater than 4
and not equal to 4
Please explain A&C

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If we use the addition property, we go from A -> B to (A -> B) V ~C (the "V" stands for 'or' and "~" stands for 'not')

Rearrange the terms to get ~C V (A -> B) and then use material implication to get C -> (A -> B). From here, use exportation to get (C & A) -> B and then use commutation to get (A & C) -> B. This derivation is pretty straightforward, but the only trick here is the addition of ~C.