Prep Test #19 Section 1 Question 13-19...Contrapositives Forum

[asics4381]

I cant wrap my head around contrapositives.

Looking at the set up for questions 13-19, the 2nd listed rule is

1. If F is 2, then G is 2

After watching, 7sage, (http://7sage.com/lsat_explanations/lsat ... -1-game-3/) he says that means the contrapositive is true meaning

If G is 1, then F is 1.

Why does this contrapositive HAVE to be true?

Why cant it be 1.F & H and 2.G or 1.F and 2. G & H

This isnt the first time ive struggled with understanding contrapositives. If someone could break this down barney style for me, I would be indebted.

[Jon McCarty]

This is a GREAT game to learn how to do contrapositives in a 2-group game. Here's a basic breakdown of contrapositives:

Given rule: If F is 2 then G is 2

Diagram: F2 --> G2

Normally you would flip the variables to the opposite side then negate them to get the contrapositive:

~G2 --> ~F2

As long as you can apply contrapositives then the underlying logic is not essential, though it is nice to understand why it works.

So if F is in 2 then G MUST be in 2. This means that if G is not in 2 then there is no way that F could be in 2 because if F was in 2 then G would HAVE to be in 2. This is the basic understanding of contrapositives.

On two group games you get a little trick that allows you to modify the contrapositive to be more useful. IF G is not in 2 then where does G have to be? Well there's only one other group, so G would have to be in 1. Similarly if F is not in 2 then it would have to be in the only other group available which is group 1.

So the original statement of ~G2 --> ~F2 is logically correct as the contrapositive but it isn't the most efficient way of writing it. Using the logic above we could write it as G1 --> F1 because if something is not in 2 then it has to be in 1. This just lets you have a better form for your contrapositives in a 2-group game.

Hope this helps! Let me know if you have any other questions on this or want something to be explained in more depth.

If you want a video explanation on this game then PM me

[asics4381]

Edit

I think I understand now.

So basically was my inference wrong that the contrapositive was limiting the following scenarios?

""Why cant it be 1.F & H and 2.G or 1.F and 2. G & H""

[Jon McCarty]

Edit

I think I understand now.

So basically was my inference wrong that the contrapositive was limiting the following scenarios?

""Why cant it be 1.F & H and 2.G or 1.F and 2. G & H""

Correct, those scenarios would be fine given the rule. If a conditional rule is going to trigger then the sufficient condition needs to occur (whether it be the given form or the contrapositive). Since the given form has F2 as sufficient and the contrapositive has G1 as the sufficient, you would need one of those two things to happen for the rule to trigger. Neither of them happens in your examples so the rule doesn't come into play.