HELP! Conditional Rules: Contrapositive Inference

Moosader

Most contrapositives makes sense to me except in the case of a negative condition, and positive reaction.

Can someone help me understand this example. (I don't think the rules are supposed to build off of each in this drill, so I've only listed the relevant one).

Scenario: A singer will perform, in order, five of seven songs: L, M, N, O, P, Q, and R.

"IF no L, then O." The answer (by negating and reversing clauses) according to a text book is "if no O, then L."

This doesn't seem true to me. There could be an L, but absence of O does not demand L. I have spent 30 minutes on this single example.

Help is greatly appreciated.

brna0714

This is a standard "either or" rule. If one is not present, the other must be. There's a great lesson on these (as well as the "not both" rules) in the 7Sage curriculum.

As far as understanding it intuitively, consider this example:

1. Original: If the store does not have apples, they'll have oranges.
2. Contrapositive: If they do not have oranges, they'll have apples.

The reason we know that they'll have apples is because if they didn't have apples, they'd have oranges and we know that they do not, in fact, have oranges.

I hope that's helpful.

ddakjiking

I'll use an apology that might make more sense.

If you're not healthy, then you're sick.

Contrapostive:

If you're not sick, you're healthy.

Moosader

Thank you both! That helped a lot

brna0714

Good! Glad to help!

Alex Short

my go to when I first started were geographical conditionals...

If you're in Albany, then you are in NY state.
If you're not in NY state, then you're not in Albany.

Or, more like your example:

If you're in Wyoming, then you aren't in San Diego.
If you are in San Diego, you aren't in Wyoming.

good luck!

Dr. Yamata

With the games and conditions like this it's also helpful to quickly notice which "side of the arrow" the negation is on and react accordingly.

~L => O
~O => L

This means that if L is out, O is in or if O is out, L is in. But notice that It's completely OK to have both L and O in. If they're both in, you don't trigger the sufficient condition of ~L or ~O.

On the other hand:

O => ~L
L => ~O

Having O in takes L out. Having L in takes O out. BUT having both L and O out doesn't trigger anything, and the rule falls away.

It may seem like a trivial or obvious distinction to some, but memorizing these little patterns will bank you serious time on test day when you don't have time to think about it.

LoraxMan

...at least one of L or O in, and possible both L and O.You cannot have both L and O out.

Classic either/or rule (or group 3 indicator) rule.

If you see this in an in/out logic game, you would write L/O in the "In" section. If you see this in LR, you know that either L or O should be valid/in/selected.