I can conclude the right logic path and get the correct answer but im still struggling on understanding while just reading it. To an extent I understand but it just feels like a mess.
I find the "choose one" part of the translation rule to add needless confusion. When both ideas aren't negated, it doesn't matter which you negate. But if the other condition is already negated, you have to pick the idea immediately after the indicator.
Why not just always pick the idea after the indicator as a rule?
So for both group 3 and group 4 I really struggle with negation. My problem is, I dont know whether I am supposed to carry the negation into the translation rule, or leave it.
for example:
flowers do NOT grow unless the garden is watered
are the two concepts /flowers and Garden watered?
and then to apply the unless rule its--
//flowers --> Garden watered?
OR
is the not part of the unless rule and its flower and garden watered so the translation is:
Something I noticed about the way negating works with these indicators is that the structure of the conditionals will always be the same based on whether one, both, or neither of the conditions are negated, regardless of which condition is sufficient or necessary
If neither is negated (eg. You will fail unless you study) only the sufficient will be negated
/X → Y
If both are negated (eg. You will not get lost unless you don't follow directions) only the necessary will (still) be negated
X → /Y
If only one is negated (eg. You can not play games unless you finish your homework) then either both conditions are the negated or neither are.
X → Y
/Y → /X
Note that X and Y are not interchangeable on this last one, so it's not as useful as the others for quickly translating, but it could still be helpful as a sanity check
I don't know how helpful this will be to anyone (myself included) so if this is more confusing, please ignore it
Why does negating the idea automatically make it the sufficient condition? How does it work out that the other idea becomes the necessary condition? I'm using the rule and it works every time, but I just don't really understand why.
"'unless' indicates a necessary condition with a negated sufficient condition"
So
A unless B
becomes
/A → B
The reason the "take either one" rule works is because when you take the contrapositive—negate both conditions and swap their relationship—you negate the condition we just negated
/B → //A
But the double negation cancels out so you're left with
/B → A
Which is the same as if you had followed the "take either one" rule, which is why it's nice to use as a shortcut so you don't need to think about this every time.
i completely got this and then you lost me and then i got it again. that was a wild ride but i think i got it? yes i'm pretty positive i understand lol
I think this question lends itself nicely to the subset, superset circles.
I imagine a big circle labeled "blackouts will occur"
Inside of that circle is a smaller circle labeled "heat wave does not abate," but that is not the only subset. For example, even if the heat wave abates, blackouts may occur because the power grid failed, or an earthquake, or something else. These would be other subsets of the "blackouts will occur" superset.
So, while the heat wave refusing to abate guarantees that blackouts will occur, the heat wave abating does not guarantee that blackouts will not occur, because a blackout could be caused by one of those other things.
this is how I solved this question, please let me know if I'm wrong because I got the confused sufficient for necessary right but my Lawgic was off.
My lawgic was BO->/HWA HWA->/BO
in earlier lesson it said if you see "unless" turn it into an "if not" statement.
Orignal: Blackouts will occur unless the heat wave abates
'IF NOT' : (suffi.) if the heat wave doesn't abate, then Blackouts will occur (Nece).
Lawgic: /HWB -> BO. /BO -> HWB
(half way through writing this I realized why my Lawgic was off...I confused sufficient for necessary conditions BRUHHH!! )
Question: which claims confused Suffi. for Necess. ? #2 is wrong b/c it flips our "if not" statement. also #1 matches the "If not" statement so it can't be that.
1) if the heat wave doesn't abate, then blackouts will occur
2) if the heat wave abate, then Blackout will not occur
this trick might not work with every "Unless" question but its still a good tool.
I dont understand when to know to take the contrapositive. When I tried the question myself I chose /HWA as the sufficient already, and thus did not need to take the contrapositive. How would I know to do that or take the contrapositive?
@taylorstryker You don't necessarily need to take the contrapositive right away. I usually start by diagramming the statement in its original form and then keep the contrapositive in mind as an equivalent version.
Whether you end up using the original conditional or the contrapositive depends on what the stimulus or answer choices give you. If an answer choice triggers the sufficient condition from your original diagram, use the original. If it gives you the negation of the necessary condition, the contrapositive may be more useful.
For example, if you have:
/BO --> HWA
the contrapositive is:
/HWA --> BO
Both statements are logically equivalent. So if an answer choice tells you heat waves do not abate, you would want to know that triggers blackouts occur (as given by the contrapositive). If it tells you blackouts do not occur, the original conditional is prob more helpful.
The main thing is not to think of the contrapositive as a separate rule that must be applied. It's just the same relationship expressed from the opposite direction. And sometimes that version will line up better with the information you're given.
Is taking the contrapositive a final necessary step to getting the correct answer? or can we translate back into English after negating one of the ideas and making it the sufficient?
@noaroxborough A contrapositive is something that is always true; it's another idea that's implied by a conditional. We don't always need to draw it out; but we do always need to understand it and recognize it.
"If A, then B."
We want to get to a point where we don't need to draw out "If Not B, then Not A" in order to understand that that follows from "If A, then B."
"Unless X, there is no Y."
That means "If Not X, then No Y" and "If Y, then X"
We want to get to a point where we don't need to draw out both of those ideas. Those statements mean the same thing and if we think of the statement as "If Not X, then No Y," we want to recognize it also means "If Y, then X" whether we draw it out or not.
It's like the idea of "X is taller than Y." Doesn't that also mean "Y is shorter than X"? Of course -- ideally we don't need to write anything out to see that. It's simply part of the meaning of "X is taller than Y"; it also means "Y is shorter than X."
i could be totally off base, but unless = "if not" was mentioned earlier right? so "blackouts will occur if not the heat wave abates" (disgusting but helpful to see) is the actual statement here. The sentence then becomes "If the heat wave does not abate, then blackouts will occur"
This threw me for a bit of a loop, but understanding wise i'm seeinng the part after the "unless" as the necessay condition while the part before is sufficient
when writing it down in lawgic, key part is unless = negate and herre negate the sufficient to get to necessary
@anamat I do too prefer whatever phrase that comes after the Group 3 indicators become the necessary condition, and the rest phrase becomes sufficient and you need to negate it. Instead of picking the idea then negating it.
209 comments
I can conclude the right logic path and get the correct answer but im still struggling on understanding while just reading it. To an extent I understand but it just feels like a mess.
If there are no more blackouts occurring, then the heat wave abated
I can't believe it's all making sense to me now! I'm ready to crush the Sept LSAT WOOHOO
I'm starting to understand sufficency necessity now I think.
i think its finally clicked for me guys
nvm
I find the "choose one" part of the translation rule to add needless confusion. When both ideas aren't negated, it doesn't matter which you negate. But if the other condition is already negated, you have to pick the idea immediately after the indicator.
Why not just always pick the idea after the indicator as a rule?
#help
So for both group 3 and group 4 I really struggle with negation. My problem is, I dont know whether I am supposed to carry the negation into the translation rule, or leave it.
for example:
flowers do NOT grow unless the garden is watered
are the two concepts /flowers and Garden watered?
and then to apply the unless rule its--
//flowers --> Garden watered?
OR
is the not part of the unless rule and its flower and garden watered so the translation is:
/flowers --> Garden watered?
Something I noticed about the way negating works with these indicators is that the structure of the conditionals will always be the same based on whether one, both, or neither of the conditions are negated, regardless of which condition is sufficient or necessary
If neither is negated (eg. You will fail unless you study) only the sufficient will be negated
If both are negated (eg. You will not get lost unless you don't follow directions) only the necessary will (still) be negated
If only one is negated (eg. You can not play games unless you finish your homework) then either both conditions are the negated or neither are.
Note that X and Y are not interchangeable on this last one, so it's not as useful as the others for quickly translating, but it could still be helpful as a sanity check
I don't know how helpful this will be to anyone (myself included) so if this is more confusing, please ignore it
Why does negating the idea automatically make it the sufficient condition? How does it work out that the other idea becomes the necessary condition? I'm using the rule and it works every time, but I just don't really understand why.
@pinky One of the ways they phrased the translation rule in the video at the start of the lesson was: (paraphrased)
So
becomes
The reason the "take either one" rule works is because when you take the contrapositive—negate both conditions and swap their relationship—you negate the condition we just negated
But the double negation cancels out so you're left with
Which is the same as if you had followed the "take either one" rule, which is why it's nice to use as a shortcut so you don't need to think about this every time.
@willdhorn Ohhh, this makes so much sense!!! Thank you for writing it out so clearly!
@willdhorn I think my senses got this but rereading this made me actually understand
i completely got this and then you lost me and then i got it again. that was a wild ride but i think i got it? yes i'm pretty positive i understand lol
@NovaBates lmao fr
Couldn't you also replace "unless" with "if not" and then evaluate the argument from there? That makes the most sense in my head.
To be clear, the rule for Group 3 applies to all indicators, correct? The example focuses on "unless" but it applies to all four.
@BoopBap Correct
I think this question lends itself nicely to the subset, superset circles.
I imagine a big circle labeled "blackouts will occur"
Inside of that circle is a smaller circle labeled "heat wave does not abate," but that is not the only subset. For example, even if the heat wave abates, blackouts may occur because the power grid failed, or an earthquake, or something else. These would be other subsets of the "blackouts will occur" superset.
So, while the heat wave refusing to abate guarantees that blackouts will occur, the heat wave abating does not guarantee that blackouts will not occur, because a blackout could be caused by one of those other things.
i get this but i also dont? like lol
this is how I solved this question, please let me know if I'm wrong because I got the confused sufficient for necessary right but my Lawgic was off.
My lawgic was BO->/HWA HWA->/BO
in earlier lesson it said if you see "unless" turn it into an "if not" statement.
Orignal: Blackouts will occur unless the heat wave abates
'IF NOT' : (suffi.) if the heat wave doesn't abate, then Blackouts will occur (Nece).
Lawgic: /HWB -> BO. /BO -> HWB
(half way through writing this I realized why my Lawgic was off...I confused sufficient for necessary conditions BRUHHH!! )
Question: which claims confused Suffi. for Necess. ? #2 is wrong b/c it flips our "if not" statement. also #1 matches the "If not" statement so it can't be that.
1) if the heat wave doesn't abate, then blackouts will occur
2) if the heat wave abate, then Blackout will not occur
this trick might not work with every "Unless" question but its still a good tool.
@YattaT I think your original lawgic is correct, why do you think you confused sufficiency for necessity?
@YattaT I think your original was correct I had the same issue but I think if you use if not you don’t have to follow the rest of the rule
I dont understand when to know to take the contrapositive. When I tried the question myself I chose /HWA as the sufficient already, and thus did not need to take the contrapositive. How would I know to do that or take the contrapositive?
@taylorstryker You don't necessarily need to take the contrapositive right away. I usually start by diagramming the statement in its original form and then keep the contrapositive in mind as an equivalent version.
Whether you end up using the original conditional or the contrapositive depends on what the stimulus or answer choices give you. If an answer choice triggers the sufficient condition from your original diagram, use the original. If it gives you the negation of the necessary condition, the contrapositive may be more useful.
For example, if you have:
/BO --> HWA
the contrapositive is:
/HWA --> BO
Both statements are logically equivalent. So if an answer choice tells you heat waves do not abate, you would want to know that triggers blackouts occur (as given by the contrapositive). If it tells you blackouts do not occur, the original conditional is prob more helpful.
The main thing is not to think of the contrapositive as a separate rule that must be applied. It's just the same relationship expressed from the opposite direction. And sometimes that version will line up better with the information you're given.
@taylorstryker So with this set of conditional indicators (like unless) I think hes saying the rule is simply you must negate.
@EricPreneta One hundred percent correct.
Very confused but I won't give up
@petvma which part are you confused about?
Is taking the contrapositive a final necessary step to getting the correct answer? or can we translate back into English after negating one of the ideas and making it the sufficient?
@noaroxborough A contrapositive is something that is always true; it's another idea that's implied by a conditional. We don't always need to draw it out; but we do always need to understand it and recognize it.
"If A, then B."
We want to get to a point where we don't need to draw out "If Not B, then Not A" in order to understand that that follows from "If A, then B."
"Unless X, there is no Y."
That means "If Not X, then No Y" and "If Y, then X"
We want to get to a point where we don't need to draw out both of those ideas. Those statements mean the same thing and if we think of the statement as "If Not X, then No Y," we want to recognize it also means "If Y, then X" whether we draw it out or not.
It's like the idea of "X is taller than Y." Doesn't that also mean "Y is shorter than X"? Of course -- ideally we don't need to write anything out to see that. It's simply part of the meaning of "X is taller than Y"; it also means "Y is shorter than X."
This is the sweetets lesson I have found on this site ever. The fact that I can pick any part of the clause and make the SC, on volition.
I cannot convey how happy this is making me RN.
Can the word "unless" be treated like the word "without" in this case?
@GregErickson97 Unless, until, and without logically mean the same thing, yes.
i could be totally off base, but unless = "if not" was mentioned earlier right? so "blackouts will occur if not the heat wave abates" (disgusting but helpful to see) is the actual statement here. The sentence then becomes "If the heat wave does not abate, then blackouts will occur"
@CScheresky Yes! Wish they pulled this earlier rule into this lesson as well instead of a new rule
man this is just giving me mind mush bro
This threw me for a bit of a loop, but understanding wise i'm seeinng the part after the "unless" as the necessay condition while the part before is sufficient
when writing it down in lawgic, key part is unless = negate and herre negate the sufficient to get to necessary
a occurs unless b occurs
/a -> b
/b -> a
@anamat I do too prefer whatever phrase that comes after the Group 3 indicators become the necessary condition, and the rest phrase becomes sufficient and you need to negate it. Instead of picking the idea then negating it.
oh yes. I get my revenge on the ice and blizzard question finally. I have been fighting to understand it for a day now.
I feel like it doesn't confuse sufficiency for necessity, more you forgot that unless means to negate.
idk if that's right lmk lol!
@Catpop Forgetting that unless means to negate is the mistake that causes one to confuse sufficiency for necessity, I think