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Say you have premise that doesn't specifically identify whether members are in or out, but is a bi-conditional like:
"Wharton serves on a different committee than the one Zhu serves on"
How do you decide which side to negate? It ends up having consequences when you chain up and try to find "or" and "not both" inferences with other members. I'm so confused.
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thank you all so so much!
2 committees....it was in/out game.
How many committees are there?
I actually wondered about this myself last week and Jonathan was kind enough to leave some really good advice: https://classic.7sage.com/discussion/#/discussion/19786/biconditionals-chaining-vs-splitting
It doesn't matter which side you negate for the chain -- I usually just do it in a way that'll make it easier to chain up the rules. But sometimes this can get messy, and so splitting is sometimes preferred.
So you know Wharton and Zhu are always apart. If there are only 2 groups then you can write it as a biconditional W(------)/Z. Because if W is in then Z is not and when W is not in, then Z is in. Now if there are 3 groups or more, you can't write this rule as a biconditional because when Z is out for example, you don't know if W is in.
Now lets say you've established its a biconditional rule, it does not matter which side you negate. You can write it as /W(--------)Z or negate the Z and not the W. As far as chaining biconditionals, I never end up doing this. When I see a biconditional connecting to other rules, I split on the biconditional so I don't have to worry about it and it makes it easier to see the "or" and "not both" inferences with other rules in the chain.