Question for "Manhattan PREP LSAT - Logial Reasoning"

[rainboots]

Pg. 90-91

It is sunny only when Sam plays outside.

In the book, it is explained that this can be written as:

If it is sunny -> Sam is playing outside

But I thought, it should be

Sam prays outside -> It is sunny

Since "Sam plays outside" is introduced with 'only when', shouldn't it be the "necessary condition"?

I am very confused with the explanation. Please help!

t

[christine.defenbaugh]

Thanks for posting, rainboots!

I think this might just be a mental labeling issue!

A conditional statement has two parts, the necessary condition and the sufficient condition. The sufficient condition is enough information to guarantee something. The necessary condition is required once we've tripped that trigger.

So, looking at the statement: If something is an apple, then it is a fruit, we can say that APPLE is sufficient information to guarantee that something in, indeed, a fruit! Alternatively, I could say that once I know something is an apple, it is necessary that it be a FRUIT!

So, the left part of the conditional statement is the 'sufficient' and the right part is the 'necessary:

If SUFFICIENT, then NECESSARY.

"Only when" does introduce the necessary condition, which is why 'sam play outside' must be AFTER the arrow.

I strongly recommend you take a bit of time to read the very beginning of Chapter 8 of the LR book, pages 342-344. I think it will help a lot in your understanding of conditional logic!

Please let me know if this helps clear up a few things!