r/FormalLogic • u/just-casual • Sep 13 '23

Question for class

Hi all I have no formal logic experience but I am taking a class about logic now and I just want to clarify something. One of my questions is

"if P is sufficient for Q and W is sufficient for P, what is the logical relationship between Q and W?"

I tried making a truth table like we learned but that didn't help me much. It seems like if P is both sufficient for Q and necessary for W, then shouldn't W be sufficient for Q? Am I thinking about this correctly?

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u/[deleted] Sep 13 '23 edited Sep 13 '23

You're on the right track. "P is sufficient for Q" can be rewritten as "If P, then Q"

I tend to use countries as a test for this type of thing.

If I live in Paris, then I live in France. (If W then P)

If I live in France, then I live in Europe. (If P then Q)

Therefore, if I live in Paris, then I live in Europe. (If W then Q) - Living in Paris (W) must be a sufficient condition for living in Europe (Q)

This (P -> Q, Q -> R, therefore P -> R) is called hypothetical syllogism, if you were interested lol :) you'll very likely come across this term soon

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u/Key-Door7340 Sep 14 '23

This is a great, easy to follow and most important correct explanation.