Q22 - No chordates are tracheophytes, and

[aileenann]

A student recently sent me this question:

I tried to diagram it using conditional logic like we did last class,
but am not sure if I'm doing it right. Here's the question:
22)

No chordates are tracheophytes, and all members of Pteropsida are
tracheophytes. [ C--> -T, P-->T ]
So no members of Pteropsida belong to the family Hominidae. [ P--> -H]

The conclusion above follows logically if which one of the following is assumed?

(A) All members of the Homimidae family are tracheophytes
(B) All members of the Hominidae family are chordates
(C) All tracheophytes are members of Pteropsida
(D) No members of the Hominidae family are chordates
(E) No chordates are members of Pteropsida


I wanted to hook together the first two statements and got: C--> -T --> -P
Not sure at this point what to do with the P--> -H statement. The
contrapositive doesnt seem to fit into the first statement H--> -P.
I ended up choosing (D) over the correct answer, (B).
Did I diagram this incorrectly?

Here's my response:
No you didn't diagram this incorrectly at all - I checked your diagramming above and it is spot on. The only thing I might have recommended is also putting in your contrapositives so you remember those possibilities as well.

Incorrect answer (D) gives you H -> -C or C-> -H. If you link that with what you have above, it will just give you C-> -T and -H. But this doesn't help us connect up P and T.

I'd point you to the way you can link things up just based on your premises already: [ C--> -T, P-->T ] If you redo these with the contrapositive, you'll see that you already know C-> -T -> -P and P -> T -> -C. So I'd say what we are really looking for to get P-> -H I think we should be looking for -C -> -H or H -> C, which is precisely what B is.

I hope that helps! Good luck with the February LSAT to those who are taking it!

[syousif3]

Why cant E be the right answer ? I agree that B is right

H-->C--> -t---> -p

But E is right as well

[timmydoeslsat]

Why cant E be the right answer ? I agree that B is right

H-->C--> -t---> -p

But E is right as well

We have H in our conclusion, but H is not in our evidence. For the conclusion to follow logically, as this question stem wants, we must have a statement with H.

Answer choice E does not have H in there.

Our argument looks like this:

C ---> ~T ---> ~P
________________
H ---> ~P

So to plug in E into our evidence will not address how H fits into this situation.

[syousif3]

Thanks so much Timmy, that makes a lot of sense now

[WaltGrace1983]

Here we have a sufficient assumption question with some great conditional reasoning exercises. The diagramming looks like this:

Premise 1: C --> ~T
Premise 2: P --> T

Conclusion: P --> ~H

Now there isn't much that we can do with just the basic setup. We need to make that inference we all known and love *drumroll* the....contrapositive!

Step 1: Link up the premises

C-->~T does not link up with P-->T but the contrapositive of P-->T makes ~T--> ~P which links up perfectly! Thus, let's rewrite the premises and the conclusion:

C-->~T-->~P
Conclusion: P-->~H

Step 2: Make the conclusion linkable too

Now what do we do from here? Once again, we take the contrapositive to figure out some more links!

P-->T-->~C

Thus, P-->~H

Step 3: Link the conclusion by finding a sufficient assumption

Now how do we conclude ~H from the premise? Well the easiest way would be to assume ~C --> ~H or that H --> C. In other words, all Hominidae are chordates. We can see that (B) perfectly links up all this stuff and restates the assumption we found!

Wrong answers

(A) H --> T. Doesn't work. It would work if we had H --> ~T or T --> ~H because this would link up.
(C) T --> P. This is an illegal reversal of what we already know.
(D) H --> ~C. So close! However, we would need H-->C to make this linkable.
(E) C --> ~P. This does nothing to help us reach the conclusion about H.

[bryan.goodpasture57]

Sorry for bringing up this question again, but had a quick question on the conditions of it.

When it says, "No Chordates are Trachs" I wrote it as ~C -> T. Is this the wrong way to write it, and if so, why?

[WaltGrace1983]

Sorry for bringing up this question again, but had a quick question on the conditions of it.

When it says, "No Chordates are Trachs" I wrote it as ~C -> T. Is this the wrong way to write it, and if so, why?

Think about what "~C --> T" says. "~C --> T" says "IF something is NOT a chordate, THEN it is a trach." From a basic level, that is not matching "no chordates are trachs." We don't know anything about those that are NOT chordates. We only things about chordates; we know that chordates are NOT trachs.

For a "No X's are Y's" type statement, think about it like this: "If you are an X, then you are NOT a Y."

Why does this work? Because the statement "No X's are Y's" is basically saying "There are NO X's that are also Y." In other words, IF you are an X, you are NOT a Y. By contrapositive, we also know that IF you are Y, you CANNOT BE an X.

Does that help? It is confusing stuff initially.

EDIT: I think a trick to this is just to say that when you have the statement "No X's are Ys," just attached the ~ to the necessary condition, thus getting (X --> ~Y.)

[bryan.goodpasture57]

That clears it up perfectly! Thanks!