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Lsatbreakingnews
Alum Member

Hi guys, I was helping my friend out with conditional logic today because I thought I had a grasp on the material but it turns out I dont....

So there was a statement from one of his textbooks he asked me to help him out with and I got it wrong.

Dmitry might play volleyball or squash, but he cant play both.

(edit meant to say might play not, might can)

So I thought great this is a bi-conditional because I see or but not both.

So I made it into: (~V <---> S) & (V <---> ~S),

But it turns out in his textbook the answer was (S -> ~V) & (V -> ~S).

So is this a different way of showing the same relationship, if so do you prefer one method over the other?

So there was a statement from one of his textbooks he asked me to help him out with and I got it wrong.

Dmitry might play volleyball or squash, but he cant play both.

(edit meant to say might play not, might can)

So I thought great this is a bi-conditional because I see or but not both.

So I made it into: (~V <---> S) & (V <---> ~S),

But it turns out in his textbook the answer was (S -> ~V) & (V -> ~S).

So is this a different way of showing the same relationship, if so do you prefer one method over the other?

## Comments

In any case, what you have there is an exclusive "or." In other words, one of the two will happen, and when it does, the other will be precluded. That is why they diagrammed it the way they did in the textbook.

In all honesty, I would have diagrammed it as a bi-conditional just like you did, simply because of the "not both" statement. But, I can see why they didn't (when you negate their diagram, it ends up looking like a bi-conditional).

It's worth noting that their translation is also redundant. Both conditionals in the conjunct are equivalent (they're contrapositives of each other).

I think this is also a case where trying to gerrymander everything into conditionals can be confusing. We think naturally in ANDs and ORs, so converting to ANDs and ORs may be more intuitive for you.

Recall that 'P -> Q' is equivalent to '~P or Q'. So, converting their translation, we have '~S or ~V'. Converting your translation, we have '(S or V) and ~(S and V)'.