Think about it like a coffee shop only has 2 employees - J and S. If J is NOT working, then S HAS to be working. If S is NOT working, then J HAS to be working. However, J and S could decide they want to work a busy shift together, so they are both working.
J or S is always in. At least one of them. So it’s possible that both J and S are in. The two rules just say “if one is MISSING, the other is in for sure.”
Only consider the thing on the left. When the thing on the left is “true”, then the thing on the right triggers.
The rules only say what happens when one of them is out. It does not say anything about what happens when one of them is in. Therefore, both of them can be in and not violate any rules.
I DON’T GET IT!!!! I’ve been staring at this in frustration for the past half hour but it’s still not clicking!!
I understand that if the thing on the left is true (if J is out), then the right triggers (S is in).
But aren’t they just contrapositives? I don’t see how they BOTH can be in. Doesn’t basically have to be either or? One or the other??
Thanks so much by the way. I feel like I won’t be able to sleep until this makes sense to me. It’s question 9 of PT33
Yes they are contrapositives. This rule basically means both of them cannot be out. AT LEAST One of them must be in.
Consider this rule:
J in —>s out.
S in —> j out
Is that the same thing as
S out —> j in
J out —> s in
??
No.
The rule only says if something is out, THEN something must be in.
Only think of as if the thing on the left is true. If the thing on the left (sufficient condition) is not met, the rule is basically meaningless.
For example, say J is in. And S is in. Does that trigger the rule??? No it doesn’t. If the rule doesn’t get triggered, don’t even waste time thinking about the rule.
It does not say If J is in, then S is out. They only deal with the negative. If J is out, then S is in. If S is out, J is in. Neither premise states the positive of "If X is in, then Y is out". If J is in, what does the rule state? It does not prohibit S's presence.
One does not have to be out for the other to be in. The sufficient condition is not required to happen - its just saying that if it does trigger, then something is required to happen.
I think your confusion stems from you assuming this is an either or rule (i.e. either J or S is in), it’s not. J and S can both be present, they just cannot both be absent. Think of it like this;
If you don’t have eggs for breakfast, you’ll have cereal.
If you don’t have cereal for breakfast, you’ll have eggs.
There is a scenario where you have both eggs and cereal for breakfast, but at least one of the two must feature in your breakfast.
I think the best way to think about it is this:
\[a\] --> \[b\]
With these logic diagrams, you are being told what happens when the sufficient condition (\[a\]/one on the left) is triggered. It's like a switch. When you flip the \[a\] switch, \[b\] will light up. This is because conditional reasoning is telling you what MUST be true.
So if you take your two rules
\~J --> S
\~S-->J
What are the switches you have... NOT j and NOT s. When you flip your \~J switch, S will light up. When you flip your \~S switch, J will light up.
Now what happens if you have S in - Which switch (sufficient condition/left side) will be triggered... Neither... none of your sufficient conditions \[switches\] have been touched and because of that they both can be in because there is not a rule that is triggered when something is in, only when something is out.
Ask yourself this. If S is in, what does it mean about J? In neither of the logical statements above does S stand as a sufficient condition. Meaning, if S is in, it does not mean that J is out. Same with J. If J is in, what does that entail about S? Absolutely nothing. Sufficient condition is not met, the rule becomes irrelevant.
I did a video on that game you might find helpful: https://youtu.be/hUBAmHpwf48. The basic idea is that if one of them is out, the other one is in, so there’s no way they’re both *out*. Since they can’t both be out, one of them must be in, and you’d want to put a placeholder for *at least* on of them on the inside. But that “at least” is important. A scenario where both J and S are in satisfies the placeholder, but doesn’t otherwise violate this clue.
A really easy way it was explained me was called a horseshoe. You have the rule and then the contra positive written directly underneath. Then there is always a third part called the horseshoe which is taking both right sides as a possibility
~j -> s (if j is not in then s is definitely in)
~s -> j (if s is not in then j is definitely in)
s - j (if s is in then j can also be in)
If you are not in the chess club you are in drama club
If you are not in the drama club then you are in chess club
this rule doesn’t say you cannot be in both clubs it only says if you are not in one you are definitely in the other.
It’s an in placeholder. That means at all times either J or S, or both are in. There’s no scenario where both J and S are out. This is the easiest way to remember what this means without unpacking the logic (which folks have already explained well in the comments).
If J is out, then S is in. If S is out, then J is in. Remember that the right side is the sufficient condition and the left side is the necessary condition. It is sufficient that J is out for S to be in, but that does not mean it is necessary. There are other possibilities in which S can be in, including a scenario where J is also in. But, since S is the necessary condition, if J is out it is NECESSARY that S is in (or vice vice versa). Therefore at all times at minimum either S or J are in, but that is not the only possibility; both can be in.
It just means at least one of them is in. If J is ruled out by another rule, S has to be in, if S is out, J has to be in. At least one has to be in, both of them can be
Think about having both J and S in. Does it trigger the first rule? Nope, because J is not out. Does it trigger the contrapositive? Nope, because S is not out. So J and S both being in is "outside the scope" of what the rule deals with.
Here's a real world situation - you have a child that must be with one of its two parents at all times. If you see Dad at the store alone, you know the kid is home with Mom. If you see Mom out picking up a cup of coffee alone, you know that Dad must be with the kid. Seeing the kid wandering the neighborhood unattended is a problem - no D, no M. That's the rule violator! But if you go to their house to visit and Dad opens the door, does that mean Mom can't also be home too? Nope. The \*problem\* is when nobody is watching the kid. It's required to have at least one parent with him, and it's fine and dandy (but not necessary) to have both.
If you just want to memorize, a friend I used to tutor with taught me this trick. Any time you write a rule and contrapositive, you can draw a big circle and a slash through it around what's on the left, and a big circle with a checkmark around what's on the right. Here, this reminds you:
No J and no S? PROBLEM (kid unsupervised)
S and J both present? That's acceptable.
When you have conditionals literally cover up the right side. Never look at it. It Doesn't exist.
When you play just ask yourself "Is J out?", "Is S out?" If it is, you get to use the clue, otherwise it doesn't do anything.
The basic thing about conditionals is that they only work in one direction. LSAC spends all of its time trying to get you to go the wrong way.
Remember, either/or has a different meaning on the lsat. It means at least one, possibly more.
I think your misunderstanding has to do with a misinterpretation of the relationship between variables in conditional reasoning. The sufficient ensures that something happens with the necessary, but the necessary can do whatever it wants independent of the sufficient. You can have a situation where the necessary of one variation on the statement happens, and then you can have the necessary of the contrapositive happen. Thus both of your variables can occur together. In your example /a -> b, /b -> a. B can happen, then later a could happen and that's fine with the rules. Also, b could happen and then a could not happen and that's also fine with the rules. Vice versa for a.
Compare this to a not both relationship. A -> /b, b -> /a. In this instance the maximum that could occur is 1 of the two, but neither could happen also. B could not happen and that would have no relationship to a. Then a could go ahead and not happen as well. Or, a could happen and since b already didn't happen that's fine. But you couldn't have a situation where both happen because the occurence of one necessarily means another didn't happen.
Hope this helps.
I love everyone trying to help. I wish I had read this months ago or thought to post. I spent 6+ hours trying to understand this very same thing. When it finally clicks, you won’t have to think about it anymore when you see the rules. You will just “get it” because you understand it. I have some tricks to getting there. There are a lot of good explanations here, but if it doesn’t quite get you there and you want to go over this for a little bit on Zoom, I’m happy to help.
I finally understand lol. It suddenly clicked in my brain before I went to bed. Yeah everyone is super helpful. I wish every subreddit had this kind of solidarity.
I wrote this.
1. You can only move from left to right.
2. You can start at any point, including S or J
3. Nothing is to the right of S or J
4. So you can deduce nothing from S or J
Suppose I say you need either cash or a credit card to pay. So if you are paying, you must have at least one.
So if you paid, and don’t have cash —> credit card
If you paid, and didn’t use a credit card —> cash
But you can have both! I didn’t say you couldn’t
Maybe you’re looking at the diagram as a whole and adding it all up like a math problem. That isn’t correct. You can start at any point. Consider this diagram
A —> B —> **~D** —> Q —> F
Suppose I tell you “D is out”. You **start** where I bolded and go left to right. We know:
D is out, Q is in, F is out
What do we know about A and B? NOTHING! They are to the left of where we start and we can’t go backwards. They could both be in or out.
Think about it like a coffee shop only has 2 employees - J and S. If J is NOT working, then S HAS to be working. If S is NOT working, then J HAS to be working. However, J and S could decide they want to work a busy shift together, so they are both working.
very good explanation!
J or S is always in. At least one of them. So it’s possible that both J and S are in. The two rules just say “if one is MISSING, the other is in for sure.”
Only consider the thing on the left. When the thing on the left is “true”, then the thing on the right triggers. The rules only say what happens when one of them is out. It does not say anything about what happens when one of them is in. Therefore, both of them can be in and not violate any rules.
I DON’T GET IT!!!! I’ve been staring at this in frustration for the past half hour but it’s still not clicking!! I understand that if the thing on the left is true (if J is out), then the right triggers (S is in). But aren’t they just contrapositives? I don’t see how they BOTH can be in. Doesn’t basically have to be either or? One or the other?? Thanks so much by the way. I feel like I won’t be able to sleep until this makes sense to me. It’s question 9 of PT33
Yes they are contrapositives. This rule basically means both of them cannot be out. AT LEAST One of them must be in. Consider this rule: J in —>s out. S in —> j out Is that the same thing as S out —> j in J out —> s in ??
But how can they both be in at the same time tho!!! One has to be out for the other to be in!! If J is in, then S is out. If S is out, then J is in!!!
No. The rule only says if something is out, THEN something must be in. Only think of as if the thing on the left is true. If the thing on the left (sufficient condition) is not met, the rule is basically meaningless. For example, say J is in. And S is in. Does that trigger the rule??? No it doesn’t. If the rule doesn’t get triggered, don’t even waste time thinking about the rule.
This is hilarious. We were all there at some point though, keep working.
I finally understand it lol. Yes it’s so damn confusing
“If J is in, then S is out” Rules don’t state this
It does not say If J is in, then S is out. They only deal with the negative. If J is out, then S is in. If S is out, J is in. Neither premise states the positive of "If X is in, then Y is out". If J is in, what does the rule state? It does not prohibit S's presence.
One does not have to be out for the other to be in. The sufficient condition is not required to happen - its just saying that if it does trigger, then something is required to happen.
I think your confusion stems from you assuming this is an either or rule (i.e. either J or S is in), it’s not. J and S can both be present, they just cannot both be absent. Think of it like this; If you don’t have eggs for breakfast, you’ll have cereal. If you don’t have cereal for breakfast, you’ll have eggs. There is a scenario where you have both eggs and cereal for breakfast, but at least one of the two must feature in your breakfast.
It is an either/or rule, but either/or rules do have the possibility of having both
I think the best way to think about it is this: \[a\] --> \[b\] With these logic diagrams, you are being told what happens when the sufficient condition (\[a\]/one on the left) is triggered. It's like a switch. When you flip the \[a\] switch, \[b\] will light up. This is because conditional reasoning is telling you what MUST be true. So if you take your two rules \~J --> S \~S-->J What are the switches you have... NOT j and NOT s. When you flip your \~J switch, S will light up. When you flip your \~S switch, J will light up. Now what happens if you have S in - Which switch (sufficient condition/left side) will be triggered... Neither... none of your sufficient conditions \[switches\] have been touched and because of that they both can be in because there is not a rule that is triggered when something is in, only when something is out.
Ask yourself this. If S is in, what does it mean about J? In neither of the logical statements above does S stand as a sufficient condition. Meaning, if S is in, it does not mean that J is out. Same with J. If J is in, what does that entail about S? Absolutely nothing. Sufficient condition is not met, the rule becomes irrelevant.
I did a video on that game you might find helpful: https://youtu.be/hUBAmHpwf48. The basic idea is that if one of them is out, the other one is in, so there’s no way they’re both *out*. Since they can’t both be out, one of them must be in, and you’d want to put a placeholder for *at least* on of them on the inside. But that “at least” is important. A scenario where both J and S are in satisfies the placeholder, but doesn’t otherwise violate this clue.
A really easy way it was explained me was called a horseshoe. You have the rule and then the contra positive written directly underneath. Then there is always a third part called the horseshoe which is taking both right sides as a possibility ~j -> s (if j is not in then s is definitely in) ~s -> j (if s is not in then j is definitely in) s - j (if s is in then j can also be in) If you are not in the chess club you are in drama club If you are not in the drama club then you are in chess club this rule doesn’t say you cannot be in both clubs it only says if you are not in one you are definitely in the other.
It’s an in placeholder. That means at all times either J or S, or both are in. There’s no scenario where both J and S are out. This is the easiest way to remember what this means without unpacking the logic (which folks have already explained well in the comments). If J is out, then S is in. If S is out, then J is in. Remember that the right side is the sufficient condition and the left side is the necessary condition. It is sufficient that J is out for S to be in, but that does not mean it is necessary. There are other possibilities in which S can be in, including a scenario where J is also in. But, since S is the necessary condition, if J is out it is NECESSARY that S is in (or vice vice versa). Therefore at all times at minimum either S or J are in, but that is not the only possibility; both can be in.
It just means at least one of them is in. If J is ruled out by another rule, S has to be in, if S is out, J has to be in. At least one has to be in, both of them can be
There is no rule against them both being in. There is a rule against both of them being out. It's just that.
Think about having both J and S in. Does it trigger the first rule? Nope, because J is not out. Does it trigger the contrapositive? Nope, because S is not out. So J and S both being in is "outside the scope" of what the rule deals with. Here's a real world situation - you have a child that must be with one of its two parents at all times. If you see Dad at the store alone, you know the kid is home with Mom. If you see Mom out picking up a cup of coffee alone, you know that Dad must be with the kid. Seeing the kid wandering the neighborhood unattended is a problem - no D, no M. That's the rule violator! But if you go to their house to visit and Dad opens the door, does that mean Mom can't also be home too? Nope. The \*problem\* is when nobody is watching the kid. It's required to have at least one parent with him, and it's fine and dandy (but not necessary) to have both. If you just want to memorize, a friend I used to tutor with taught me this trick. Any time you write a rule and contrapositive, you can draw a big circle and a slash through it around what's on the left, and a big circle with a checkmark around what's on the right. Here, this reminds you: No J and no S? PROBLEM (kid unsupervised) S and J both present? That's acceptable.
When you have conditionals literally cover up the right side. Never look at it. It Doesn't exist. When you play just ask yourself "Is J out?", "Is S out?" If it is, you get to use the clue, otherwise it doesn't do anything. The basic thing about conditionals is that they only work in one direction. LSAC spends all of its time trying to get you to go the wrong way.
Remember, either/or has a different meaning on the lsat. It means at least one, possibly more. I think your misunderstanding has to do with a misinterpretation of the relationship between variables in conditional reasoning. The sufficient ensures that something happens with the necessary, but the necessary can do whatever it wants independent of the sufficient. You can have a situation where the necessary of one variation on the statement happens, and then you can have the necessary of the contrapositive happen. Thus both of your variables can occur together. In your example /a -> b, /b -> a. B can happen, then later a could happen and that's fine with the rules. Also, b could happen and then a could not happen and that's also fine with the rules. Vice versa for a. Compare this to a not both relationship. A -> /b, b -> /a. In this instance the maximum that could occur is 1 of the two, but neither could happen also. B could not happen and that would have no relationship to a. Then a could go ahead and not happen as well. Or, a could happen and since b already didn't happen that's fine. But you couldn't have a situation where both happen because the occurence of one necessarily means another didn't happen. Hope this helps.
I love everyone trying to help. I wish I had read this months ago or thought to post. I spent 6+ hours trying to understand this very same thing. When it finally clicks, you won’t have to think about it anymore when you see the rules. You will just “get it” because you understand it. I have some tricks to getting there. There are a lot of good explanations here, but if it doesn’t quite get you there and you want to go over this for a little bit on Zoom, I’m happy to help.
I finally understand lol. It suddenly clicked in my brain before I went to bed. Yeah everyone is super helpful. I wish every subreddit had this kind of solidarity.
I wrote this. 1. You can only move from left to right. 2. You can start at any point, including S or J 3. Nothing is to the right of S or J 4. So you can deduce nothing from S or J Suppose I say you need either cash or a credit card to pay. So if you are paying, you must have at least one. So if you paid, and don’t have cash —> credit card If you paid, and didn’t use a credit card —> cash But you can have both! I didn’t say you couldn’t Maybe you’re looking at the diagram as a whole and adding it all up like a math problem. That isn’t correct. You can start at any point. Consider this diagram A —> B —> **~D** —> Q —> F Suppose I tell you “D is out”. You **start** where I bolded and go left to right. We know: D is out, Q is in, F is out What do we know about A and B? NOTHING! They are to the left of where we start and we can’t go backwards. They could both be in or out.