PT9.S2.Q23 - a poor farmer was fond of

TexAgAaron

So I got this one wrong and picked C when A is the correct AC. It's just not clicking for me how this is correct. Any help would be greatly appreciated!

Blake160

I'll give it a shot.

"Either" is typically an /A > B relationship. But in this context, I assumed that one cannot be both "honest and dishonest" or both "rich and poor." Under this interpretation, it becomes two biconditionals:

/poor <---> rich
/honest <--->dishonest

Resulting in a chain that looks like this, with the red arrow being the sufficient assumption that validates the conclusion (reading right to left):

http://i.imgur.com/2iRVTrP.png

TexAgAaron

@Blake160 I don't think I follow your diagram. I understand that you can't be rich and poor, and be honest and dishonest. I don't get the logical chain you used though. I don't think I've actually ever seen a diagram like that before.

Blake160

@akeegs92

Ignoring the distinction between rich/poor and honest/dishonest, you still have:

Premise: Poor --> Honest

Conclusion: Rich ---> Dishonest, which can be interpreted as: /poor ---> /Honest

This isn't a valid conclusion from the premise P --> H, but becomes valid if you add H--->P to make P<------>H. Then, if /P then /H.

TexAgAaron

I sorta follow. I'm just lost when you make the jump from a conditional to a bi-conditional. I don't quite understand the process there.