Conditional linkage

Terry Wrist

If I have a statement: A ---> C
and a second statement: B ---->C
is it fair to say A + B ----> C?

Logician

No- here’s why. While it would be true in that if you have A and B then you must have C, that logical representation would be excluding two other valid possibilities:
1) just A
2) just B

Both of these possibilities are sufficient for concluding C. So while it would not be inaccurate per say to represent it as A + B —> C, it would be an incomplete representation of the logical relationship, seeing as it’s excluding two other possible worlds (only represents 1/3 of the worlds).

the correct representation would be:
A or B —> C

In this representation, 3 possibilities exist that are each sufficient to trigger the necessary.
1) just A
2) just B
3) A and B

LOWERCASE EVERYTHING

it might be helpful if you look at the contrapositives. the correct inference is /c --> /a and /b which is totally different from the incorrect inference: /c --> /a or /b.

by the way, you can also conclude: /a some /b