Like the Birds in the Forest Logic Game, this is an In-Out game where the rules can be connected to form long conditional chains.

I designate bills voted "For" as being "In" (positive). I designate the bills voted "Against" as being "Out" (negative).

If you're new to this, or you need a reminder, sufficient is before the arrow, and necessary is after the arrow: Sufficient -> Necessary (see this for more details).

First rule:

G only if NOT E can be diagrammed as

("only if" introduces the necessary condition)

The contrapositive, would be:

Second rule:

(I skip this rule because it mentions variables not mentioned in the first rule. Put a mark next to this rule as a reminder to come back to it.)

Third rule:

This means at least one of E and J must be in, but there's no reason we can't have both in.

This can be diagrammed as:

NOT E -> J

Contrapositive:

NOT J -> E

By connecting this rule (and its contrapositive) to the first rule (and its contrapositive), we get:

and

Second rule:

Now that we have J on our diagram, it's worth taking a look at the second rule because we'll be able to connect the variables in this rule to what we already have on our diagram.

The word "unless" is tricky, but I've recently explained it here.

If you like, you can switch the order of the clauses in this rule in order to think of the rule as "I unless NOT J"

This becomes "NOT I -> NOT J"

Contrapositive:

J -> I

We can immediately connect this rule (and its contrapositive) to what we've already diagrammed, giving us:

and

Fourth rule:

If introduces the sufficient condition, so it should really be thought of as:

H + D -> G

(H and D being in are sufficient to guarantee that G is in.)

Contrapositive:

NOT G -> NOT H or NOT D

On the diagram, it becomes:

Remember that the word "or" is inclusive. This means that if G is out, at least one of H and D will be out, but perhaps both of them will be out.

For the "or," some people like to use a dotted-line arrow rather than a solid line and writing the word "or." With a dotted-line arrow, this rule would look like:

Either way is fine - as long as you know what it means.

Question 7's rule:

Question 7 adds a new rule: F --> NOT J

Take the contrapositive: J --> NOT F

Add both to the diagram, and you get:

***

With the rules correctly diagrammed in these chains, you should be able to get through the game's questions on your own. Most of the difficulty is in setting up the game and forming the chains.

I talk about how to read this type of diagram in my explanation of the LSAC-written Birds in the Forest Logic Game.

Photo by wallyg / CC BY-NC-ND 2.0

I love it!!! It unlocked my mimd!!! Thanks Steve!!!

ReplyDeleteNow you're teaching a man how to fish...

ReplyDeleteyou're my LSAT guru. (very low bow)

ReplyDeleteHello, and thank you for your blog!

ReplyDeleteI'm having a lot of trouble with the second rule,

"Unless she votes against the judicial activism bill, she will vote for the immigration bill."

Rephrased, "I unless NOT J"

which I transcribed as

¬J --> ¬I (if she votes against J, she will vote against I)

and the contrapositive, I --> J (if she votes for I (sufficient), it will mean that she will vote for J (necessary))

although I can see how "I unless NOT J"becomes "NOT I -> NOT J" (If she doesnt vote for I it means that she hasn't voted for J), I don't see the problem with my transcription, which really messed up my diagram as a whole. How should I have known to use "NOT I -> NOT J", and thus J-->I? Help!

Thank you!

With conditional rules that have 'unless', the condition after the word unless is the necessary condition (in this case, "she votes against the judicial activism bill. i.e. NOT J) is the necessary condition, and then you negate the second part/condition and make this negation the sufficient condition (in this case, "She will vote for the immigration bill" negated becomes "NOT I").

DeleteThis way you get a NOT I --> NOT J

Conceptually, and the way I understand it is that: "Unless she votes against the judicial activism bill, she will vote for the immigration bill" means that the norm is that she will vote for the immigration bill, unless she votes against the judicial bill, in which case (this UNLESS exception) she votes AGAINST the immigration bill. Thus voting against the judicial bill (NOT J) is a necessary condition for her deviating from her norm (which was 'voting for') and instead voting against the immigration bill (NOT I)

But why does "Unless" indicate that she will NECESSARILY vote against the immigration bill if she votes against the judicial activism bill?

DeleteLet's assume she votes against J - the game expects you to assume that she must also vote against I. But the truth is she can still vote for I, since the condition mentioned in the rule (unless she votes against J) doesn't apply.

In other words, the rule basically says "Unless she votes against J, she will DEFINITELY vote for I."

But it doesn't say that she will definitely NOT vote for I if she votes against J. This is an assumption we are making, but I can't see what we're basing that on, beyond intuition vis-a-vis the word "unless."

Similarly, I transcribed "She votes for the gun control bill if she votes for both the health care bill and the defense bill" as

ReplyDeleteG-->H (H is necessary for her to vote for G)and

G-->D (D is necessary for her to vote for G)

with the contrapositives

¬H-->¬G (if she doesn't vote for H, then she won't vote for G)and

¬D-->¬G (if she doesn't vote for D, then she can't vote for G).

Once again, I see how your transcription is right, but I don't see how mine is wrong. How should I have known not to use it?

Thank you!

4. If the legislator votes against the immigration bill, then which one of the following is the minimum number of the seven bills she must also vote against?

ReplyDelete(A) one

(B) two

(C) three

(D) four

(E) five

Here the questions says which one of the following is the minimum number of the seven bills she must also vote against.

Wouldn’t the usage of the word also imply that in addition to the immigration bill she must only vote against two other bill, since if you vote against the immigration bill then the minimum number of bills you must vote against is three in total. So shouldn’t the answer be two instead of three?

I was also confused by the wording of this question. I chose "D," or Four minimum. Here was my reasoning:

DeleteShe votes for the gun control bill only if she votes against the environment bill.

[G --> ~E]

Unless she votes against the judicial activism bill, she will vote for the immigration bill.

[J --> I]

She will vote for either the environment bill, the judicial activism bill, or both.

[E or J]

She votes for the gun control bill if she votes for both the health care bill and the defense bill.

[(H&D) --> G]

Valid inferences from the rules:

E or I

(H&D) --> ~E

(H&D) --> (I&J)

I mainly ran the modus tollens a bunch. From ~I it follows that ~J; from ~J it follows that E; from E it follows that ~G; from ~G it follows that either ~H or ~D.

So the minimum is 4: ~I + ~J + ~G +~H/D. That's four. It's only 3 if the question meant to as say something like "minimum in addition to I." If so, then it's 3, not 4. But it didn't say that. Where did I go wrong?

Sorry, I meant to say, "minimum in addition to ~I."

DeleteThe toughest question for sure was the 1st one, your diagram makes the rest a piece of cake.

ReplyDeleteU R BRILLIANT...

Thank you, Steve.

ReplyDeleteYour blog has been so helpful while I continue to pound out the LSAT questions. I seem to have difficulty answering the "Which one of the following could be a complete and accurate list..." types of questions such as Q1. Your diagram made the rest easy to answer. For some reason I do not understand how to get to the correct answer choice (E). Any suggestions?

Thank you!

Dan

I was confusing the 'in' and 'out' groups which made me unable to answer question 1. Once I realised that Questions one asks about the 'out' (voting against' group), things fell in place.

Delete:)

Hi Steve,

ReplyDeleteI'm having the same trouble as Dan!

Hi,

ReplyDeleteShouldn't the correct answer for question 1 be A?

I believe E is incorrect because if she votes for gun control, then she does not vote for environment.

Am I missing something?

Thanks

I was having the same issue with #1, but I think i figured it out...the answer is E because the rule "She votes for the gun control bill only if she votes against the environment bill." means that they can't both be in. It doesn't mean they can't both be out.

ReplyDeleteI thought the answer might be A too, but it violates the rule "She votes for the gun control bill if she votes for both the health care bill and the defense bill." Since G is out, then D or H (or both) must also be out.

...at least I'm hoping I figured it out!

i think the keys to getting question #1 are:

ReplyDelete1) noticing the stem indicates AGAINST. otherwise, if you misread and take this question to be about bills voted FOR, then rules like the first one will trip you up and eliminate what would otherwise be correct answer (E).

2) thinking in terms of IN/OUT. by that i mean, for each bill voted AGAINST, that must mean all those NOT mentioned must be bills that are voted FOR.

This comment has been removed by the author.

ReplyDeleteHey guys,

ReplyDeleteI was wondering if someone could explain the 2nd rule, "Unless she votes against the judicial activism bill, she will vote for the immigration bill." I"m confused about how it turns into J--I?

From my understanding of Steve's tips, you would turn Unless into If not. So is my thinking correct if I then consider the rule as, "If not voting against judicial activism, she will vote for the immigration bill." By turning the sufficient statement into a double negative, it becomes a positive? Sorry for the terrible phrasing, LSAT speak doesn't translate very well into regular English.

How can "only if" introduce a necessary condition and "if" introduce a sufficient condition? Why doesn't "only if" introduce a sufficient condition?

ReplyDeleteSteve Swartz can you please explain the answer to #1?

ReplyDeleteCan someone explain to me why G is necessary condition and H+B sufficient. This point is confusing me so much.thanks.

ReplyDeleteI need some help figuring out how E is the correct answer for question 1. Based on the rules, I arrived at the conclusion that the following is a complete and accurate list of bills that could be voted against:

ReplyDeleteF, I, J, G, H, D.

In answer E, if gun control (and thus health care and defense) is voted against, it follows that J and I are voted against as well, right?

I think there is an inaccuracy in this question with regard to the rule

ReplyDelete"Unless she votes against the judicial activism bill, she will vote for the immigration bill."

The game expects you to derive that I and J must always be paired together from this rule. But that is inaccurate:

Let's assume she votes against J - the game expects you to assume that she must also vote against I. But the truth is she can still vote for I, since the condition mentioned in the rule (unless she votes against J) doesn't apply.

In other words, the rule basically says "Unless she votes against J, she will DEFINITELY vote for I."

But it doesn't say that she will definitely NOT vote for I if she votes against J. This is an assumption we are making, but I can't see what we're basing that on, beyond intuition vis-a-vis the word "unless."

Maybe I'm missing something? Can anyone help out? Thanks!