Hi, could you explain under which circumstances could we break up a compound S&N condition?
If it is something like all small countries and coastal countries like apples, then in that case we can break up the statement into two conditionals, right?
What if it was all small countries like apples and bananas? Could that be broken up into two conditionals?
Similarly, what if it was if you like bananas or apples, then you are from a small country? Could that be broken up into 2?
And what if it was everyone from a small country likes apples or bananas? Can that be broken up?
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These are good examples, I will go through them and explain.
"All small countries and all coastal countries like apples." We could diagram this as separate statements, because each sufficient condition alone will bring about the necessary. It is effectively saying, "If a country is small or coastal, then its people like apples." SC ---> LA CC ---> LA or we could diagram them together SC or CC ---> LA Why "or"? Because just one of these sufficient conditions will lead to the necessary condition, which is why they can stand alone as well.
Note that small word changes can make a difference here. "All small, coastal countries like apples." This cannot be separated into two, because the sufficient condition effectively says "small and coastal." Just one sufficient condition will not guarantee the necessary. SC & CC ---> LA
"All small countries like apples and bananas." Again, we could write this separately. SC ---> LA SC ---> LB or SC ---> LA and LB Why "and"? Because both necessary conditions must follow from the sufficient.
"If you like bananas or apples, then you are from a small country." This is just like your first example. LA or LB ---> SC or LA ---> SC LB ---> SC
"Everyone from a small country likes apples or bananas." This one cannot be broken up. (SC ---> LA) cannot stand alone, because we cannot make the conclusion that this person likes apples. It is just as possible that they like bananas. This is one statement: SC ---> LA or LB
If I can think of a general rule: "or" in the sufficient can be separated, but "or" in the necessary cannot. "and" in the necessary can be separated, but "and" in the sufficient cannot.
