Logical Reasoning Question Forum

[Bilqis]

Hello everyone

Could somebody please explain to me this logical relationship:


If no J then S

Does that mean if J is there that S cannot be there?

Thank you

[mmm2602]

No.

"If (not J) then S" implies "if (not S) then J", not "If J then (not S)"

[Bilqis]

Thanks a lot, that was helpful!

[Bilqis]

Okay this is a tough one, could you or anybody tell me why the answer to the following is A?

If there are any inspired musical performances in the concert, the audience will be treated to a good show. But there will not be a good show unless there are sophisticated listeners in the audience, and to be a sophisticated listener one must understand one's musical roots.


A) If there are no sophisticated listeners in the audience, then there will be no inspired musical performances in the concert

[Bilqis]

This rule is a difficult concept for a lot of people. It's weird to think the absence of something triggers the presence of something else.

The rule is: if no J, then S

Diagrammed as such:

J -----> S

via the contrapositive:

S -----> J

The presence of the necessary condition does not have to preclude the sufficient condition. Or, simply, you can have one, the other, or both. They can just never BOTH be absent

So one of them always has to be there. Think of it this way: it's like two parents share responsibility to pick their kids up from school. Someone always has to be there, or their kid has no way to get home. There are three possibilities:

Mom picks kids up
Dad picks kids up
Mom and dad pick kids up together

Hope this helps. It's a weird rule at first.

Thank you so much, very helpful!

[btowncane]

Okay this is a tough one, could you or anybody tell me why the answer to the following is A?

If there are any inspired musical performances in the concert, the audience will be treated to a good show. But there will not be a good show unless there are sophisticated listeners in the audience, and to be a sophisticated listener one must understand one's musical roots.


A) If there are no sophisticated listeners in the audience, then there will be no inspired musical performances in the concert

Basically you can break that stem down into three conditional statements where:
IMP = Inspired musical performance
GS = Good show
SL = Sophisticated listeners

Also, keep in mind that "unless" changes the affected condition to "if not".

1. IMP → GS
Contrapositive (CP): ~GS → ~IMP

2. ~SL → ~GS
CP: GS → SL

3. SL → UMR
CP: ~UMR → ~SL

Then combine the relationships starting with not sophisticated listeners and you get:

~SL → ~GS → ~IMP

Which is a longer way of saying:

~SL → ~IMP

Hope this helps.

[Bilqis]

Btwocane


That was very helpful, thank you

[LoveLife89]

It basically means it has to be one or the other. It could be both but at least one of them has to always be included

[bp shinners]

Negating the sufficient condition creates an "at least one" relationship. That's the most straightforward way I have found to explain this concept.

[Bilqis]

Thank you all for replying! It's clearer to me now