Q23

ManhattanPrepLSAT1
Atticus Finch

Posts: 2851
Joined: October 07th, 2009

Q23

moshemeer
Vinny Gambini

Posts: 11
Joined: May 03rd, 2016

Re: Q23

why is E not the same as C?

ohthatpatrick
Atticus Finch

Posts: 4257
Joined: April 01st, 2011

Re: Q23

(E) is just an illegal reversal of the rule we're replacing.

~K --> H and M

and (E) says
H and M --> ~K

Are you familiar enough with conditional logic to know what I mean by an illegal reversal?

The same answer applies to why (E) and (C) are different.

(C) starts with ~K

(E) ends with ~K

priyanka.krishnamurthy
Vinny Gambini

Posts: 16
Joined: November 29th, 2015

This post thanked 1 time.

Re: Q23

Quick question on E... I use the 'if not' = 'unless' method when diagramming unless. I just want to confirm that 'if not either H or M' would translate to 'if neither H and M' That's the only way I am getting that mistaken reversal & I just want to make sure I got that straight going forward.

Diagram:
~H and ~M -> T

Thanks!
pK

ohthatpatrick
Atticus Finch

Posts: 4257
Joined: April 01st, 2011

This post thanked 1 time.

Re: Q23

Sorry for the delayed answer to the quick question:

YES, when we say “if not” before a compound idea, such as “H or M”, you’re saying “If that compound idea is not the case”, which is essentially the same as doing what you’d normally do when you negate ‘H or M’ to write a contrapositive.

IF NOT “H or M” = ~H and ~M
IF NOT “G and ~F” = ~G or F

In fact, the method some people use for “unless” is to just write the two ideas in the sentence as the two right side ideas.

Given:
Unless either H or M goes to T, K goes to T

We could write:
---> Ht or Mt
---> Kt

And then just contrapose those to see the left sides:
…………….~Kt --> Ht or Mt
~Ht and ~Mt --> Kt

More conversationally, you can think, “What has to be true for it to NOT BE THE CASE that either H or M is assigned to T? I guess they would BOTH have to be NOT ASSIGNED to T.”

YuriJ257
Vinny Gambini

Posts: 7
Joined: July 21st, 2018

Re: Q23

I thought it was both F and M must be T unless K is T which translates to:
if F & M are ~T, K is T.
if K is ~ T, F or M are T.

SO, if F OR M can be T if K is NOT T, then it could be:

S T
K M
F G
H
L

ohthatpatrick
Atticus Finch

Posts: 4257
Joined: April 01st, 2011

Re: Q23

You said:
I thought it was both F and M must be T unless K is T which translates to:
if F & M are ~T, K is T.

That's incorrect. "unless" always means "put the negated version of this idea on the left side of the arrow",

Unless X happens, Y happens
~X --> Y

G happens, unless H doesn't happen
H ---> G

M happens, unless P and K happen
~ (P and K) --> M
which means ...
~P or ~K ---> M

Because of that,
(C) would be written like this:
~Kt --> Ft and Mt

is that the same as the original rule?
~Kt ---> Ht and Mt

It's pretty close, other than switching Ft and Ht.
But wait! Since there is a rule that F and H are always in the same group, those mean the same thing!

Thus, it is the same rule.

Incidentally, this is the biggest pattern so far for correct answers to Equivalent Rule questions: whichever rule they're asking us to replace contains some character (A) who is in SOME OTHER rule, inextricably bound up with some other character (B).

The correct answer re-writes the original rule by swapping out A for B.

For example, if you had these two rules:
F - J
and
GJ

Then if they asked us to replace "F - J", the correct answer would likely be "F - G".

Hope this helps.