Can someone explain why this is an invalid inference??

[TheNewGuy]

Testmaster book #4, Pg.46


This is the rule that I got screwed up on...I'm still trying to figure this stuff out...


"F cannot be on the same committee as K"

 F< -|->K

"If K is on a committee, J must also be on that committee"

This is possibly where I got screwed up...I wrote...

K -> J

Then I took what I think is the contrapositive....If not J then not K, which I took to mean J -> K

From this I made the inference that F<-|->J....which is apprently an invalid inference...can someone please explain why. I think I'm finally close to understanding this stuff, I just need a little help...thanks!

[NYKnicks]

If not J then not K doesn't mean that J->K
This means that if J is not present in the committee, then there is no way for K to be present in the committee without J.
It doesn't say anything about J being in the committee alone without K though.

Testmaster book #4, Pg.46


This is the rule that I got screwed up on...I'm still trying to figure this stuff out...


"F cannot be on the same committee as K"

 F< -|->K

"If K is on a committee, J must also be on that committee"

This is possibly where I got screwed up...I wrote...

K -> J

Then I took what I think is the contrapositive....If not J then not K, which I took to mean J -> K

From this I made the inference that F<-|->J....which is apprently an invalid inference...can someone please explain why. I think I'm finally close to understanding this stuff, I just need a little help...thanks!

[Matthew_24_24]

You cannot deny the premise and affirm the conclusion.  That is a logical fallacy.

You can deduce from that:

F --> ~(j or k)

[shaz]

This is explained in detail in the nova book. It's a typical necessary for sufficient mistake.

If you review this and causation you'll be straight. It seems tricky but you get the hang of it quick. Wait until parellel reasoning and paradoxes.

Be able to recognise the common fallacies and you'll be fine.