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### Those who are great in Discrete Math/Structures, help me understand this truth table!

Ok... I have this table of truths for p and q.
When p implies q, it's easy to understand, but I don't understand q->p

https://imgur.com/a/x3Sro

 Not being in France is a consequence of being in Paris: TRUE

I don't understand this because a consequence of being in Paris, means you have to be in France. So shouldn't it be FALSE?

 Being in France is a consequence of not being in Paris: FALSE

Again, I don't understand this. Couldn't you be anywhere in France? You're not limited to Paris.

Am I not understanding something here? Am I misunderstanding the whole thing of q->p? Please guide me in the right direction. I've been trying to understand this for such a long time. Unfortunately, all the videos I've watched do not seem to help.

This is the truth table, for general things I guess.
https://imgur.com/a/JrFwK
Last edited on
Looks like you understand just fine. Only one of p -> q or q -> p can be accurate if either even apply.
The textual descriptions confuse me, but if you just look at the truth values T->F should be the only one that is false, and as you can see it is the case for both of them.

The second table, q->p (in France implies in Paris), doesn't makes much sense in the real world if we are talking about the location of a tourist because there are more places than Paris to visit, but if the context is for example some country's embassy, and it only got one in France located in Paris. Being at that country’s embassy in France would then imply that I'm in Paris.
 Only one of p -> q or q -> p can be accurate if either even apply.

p->q and q->p implies that p and q are equivalent.

((p→q)∧(q→p)) → (p↔q)
Last edited on
Yes. The OP's example didn't bring that to mind since they're clearly not equivalent. I should've noted my assumption that p and q are not equivalent.

Thanks for the correction.
Thanks to both of you! After a long time of thinking and countless table drawings, it finally made sense.
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