Multiple Compound Terms in Conditional Reasoning

[SLF]

Given the following...

"If it is not the case that the park contains both L and O, then it contains F and S."

Based on this, it makes sense to me that If I have neither L nor O, then I must have both F and S.

But, what if I have L but not O then must I still have both F and S?

Likewise, if I have O but not L then must I still have both F and S?

Thanks for your help.

[Ron Gore]

Hi, SLF!

Thanks for your question. You've definitely identified a tricky conditional statement. Your statement was:

"If it is not the case that the park contains both L and O, then it contains F and S."

The sufficient condition in this relationship is that the park does not contain BOTH L and O. This does not mean that both L and O are absent from the park, but rather that at least one of them is absent. So, relationship is:

L F

.....OR AND

O .....S

The contrapositive of this relationship is that if either F or S is absent, then both L and O must be present.

F L

.....OR AND

S .....O

I hope this helps. Please let me know if I may assist you further.

Ron

[SLF]

I deeply appreciate your prompt reply.

I was making the the sufficient condition an 'and' relationship and that was where I was off track.

Thank you.