Really basic questions

datanully

I have gone through the course and watched all the LG videos and done most of the problem sets but I'm still unclear on a few things. I know this stuff is basic but I am really not smart.

So say there is a rule in a sequencing game if x is 3rd then y is 5th. Does that mean is y is 5th, then x has to be 3rd? I keep thinking the answer is no. Or if it is an in and out game. If X is in, then Y is in. I know the contrapositive is if X is out, y is out but what about if I only know y is in. Does that mean x has to be in as well or can y be in by itself.

I really don't get lawgic and can't follow when JY starts writing formulas. I'm sure his explanations are great, my brain just cannot process them. It doesn't work right. I've got extra time accommodations for the actual test but I still don't come close to finishing LG.

Heinz Doofenshmirtz

Hi!

To answer your question about x being in third and y being in fifth:

If x is in third, then y is in fifth
Contrapositive: If y is not in fifth, x is not in third.

To find the contrapositive of a statement, the "formula" for doing it is to swap the two sides of the arrow and negate both. So for the second statement you made (if x is in, then y is in), the contrapositive is: if Y is not in, X is not in).

You asked: " I know the contrapositive is if X is out, y is out but what about if I only know y is in. Does that mean x has to be in as well or can y be in by itself."
The contrapositive you wrote is incorrect, but to answer your question, with the original statement (If x is in Y is in), if all we know is Y is in, then we do not know anything about X. It could be in, and it could be out.

You stated: "So say there is a rule in a sequencing game if x is 3rd then y is 5th. Does that mean is y is 5th, then x has to be 3rd? I keep thinking the answer is no."

You are correct! The answer is no. All we know from the given rule is the original statement (If x is in 3rd then y is in fifth) and the contrapositive (if y is not in fifth, x is not in third), nothing more.

The "formula" I mentioned works but I really think you should only use it when you understand the reasoning behind why a contrapositive works. To do this you could review JY's video on it, or maybe read the section on contrapositives in the LSAT Trainer by Mike Kim (that helped me a lot). If I find a good video on contrapositives on Youtube, I will post it in another comment.

BUT I just wanted to wrap up by saying that while your post had a minor error in the contrapositive, to me the biggest error is in saying that you're "really not smart" !. This test isn't intuitive for a lot of us, so if something isn't clicking don't put yourself down like that. You can and will do it.

studyingandrestudying

There's a youtube video you might find helpful called why the LSAT can make smart people feel not smart or a similar title.

cantmakeupmymind

You were half right - you're correct in your first (sequencing) example, but incorrect on your second (in/out) example. To find the contrapositive, flip and negate. Here's what that means:

You gave the example of "If X is 3rd, then Y is 5th."
X in 3rd is your sufficient condition (left side), Y in 5th is your necessary condition.

X3 -> Y5

To flip them, you move them to the opposite sides of the lawgic equation - X3 moves to the right side (necessary side), Y5 to the left side (sufficient side). But to get the contrapositive, you also have to negate them. It becomes:

/Y5 -> /X3

(If Y is not 5th, then X is not 3rd.)

These are the only statements you can come up with from that initial statement ("If X is 3rd, then Y is 5th.") The sufficient condition triggers the necessary condition, but the mere presence of the necessary condition doesn't actually tell you anything about the sufficient condition. If you know Y is 5th, that doesn't tell you anything about X - it could be 3rd, or it could be in another position. Similarly, if you know X is NOT 3rd, that doesn't tell you anything about Y - it could be 5th, or it could not be. The right side of your lawgic equation doesn't do anything to the left side.

For your In/Out example, the contrapositive of X in -> Y in IS NOT X out -> Y out. Please don't do that to yourself! You've got to flip your variables and negate them, and in this case you didn't flip them. Here's the lawgic for "If X is in, then Y is in."

X -> Y
/Y -> /X

(in other words:
X in -> Y in
Y out -> X out)

X out is on the right side. It's the necessary condition. It doesn't tell you anything about Y.
(Y in also doesn't tell you anything about X. But Y out tells you that X is out.)