Prepare for the LSAT or discuss it with others in this forum.
jjinva

Posts: 65
Joined: Tue Oct 27, 2009 4:55 pm

I understand what they are, obviously. To a degree I guess.

I get what I think is the basics. Here are examples. Am I right? Rule then contrapoz below:

If L then T
If -T then -L

If L then not T
If T then -L

If L then R and T
If -R OR -T then -L

If L then not R or T
If R AND T then -L

Do those look right so far?

Where I am missing something key (or have forgotten it since I last studied a few months ago) is the meanings of things like "neither R nor T" and its contrapoz and the contrapoz of the IF and ONLY IF stuff.

Is there a place online that has that stuff written out somewhere. I am using PS LG Bible and going through the games, and I am finding when I get things wrong its because I am not writing rules/contras correctly, especially on the AND/OR things and NEITHER/NOR things.

So I am missing an obvious "a-ha!" moment that is probably something a 3rd grader would get! Thanks for your help.

pattymac

Posts: 210
Joined: Wed Nov 04, 2009 7:44 pm

### Re: generic question about contrapositives

For this type of stuff, I don't think it matters what the arguments say because you have to accept it as true in the LSAT world. What helped me was looking past what they said and knowing how to diagram them. At first I was wasting my time worrying about whether or not it made sense, but thats how you get tripped up.

Heres a sweet example I found that helped me.

if I live in Cleveland, I live in the USA.

CONTRAPOSITIVE: I don't live in the USA, so I don't live in Cleveland.

MISTAKEN NEGATION: I don't live in Cleveland, so I don't live in the USA.

MISTAKEN REVERSAL: I live in the USA so I live in Cleveland.

Just focus on diagramming these things quickly and not reading too far into them.

jjinva

Posts: 65
Joined: Tue Oct 27, 2009 4:55 pm

### Re: generic question about contrapositives

pattymac wrote:For this type of stuff, I don't think it matters what the arguments say because you have to accept it as true in the LSAT world. What helped me was looking past what they said and knowing how to diagram them. At first I was wasting my time worrying about whether or not it made sense, but thats how you get tripped up.

Heres a sweet example I found that helped me.

if I live in Cleveland, I live in the USA.

CONTRAPOSITIVE: I don't live in the USA, so I don't live in Cleveland.

MISTAKEN NEGATION: I don't live in Cleveland, so I don't live in the USA.

MISTAKEN REVERSAL: I live in the USA so I live in Cleveland.

Just focus on diagramming these things quickly and not reading too far into them.

Thanks. What about NEITHER NOR and IF AND ONLY IF contrapositives?

scionb4

Posts: 503
Joined: Mon May 26, 2008 8:57 am

### Re: generic question about contrapositives

According to the label, contrapositives are at best 98% effective, and that's only when used properly according to the numerous guidelenes.

The Pen Is Mightier

Posts: 140
Joined: Fri Oct 16, 2009 1:18 pm

### Re: generic question about contrapositives

The only contrapositive is abstinence!

scionb4

Posts: 503
Joined: Mon May 26, 2008 8:57 am

### Re: generic question about contrapositives

The Pen Is Mightier wrote:The only contrapositive is abstinence!

Well, at least it's the only 100% fool-proof contrapositive.

The Pen Is Mightier

Posts: 140
Joined: Fri Oct 16, 2009 1:18 pm

### Re: generic question about contrapositives

scionb4 wrote:
The Pen Is Mightier wrote:The only contrapositive is abstinence!

Well, at least it's the only 100% fool-proof contrapositive.

Well saying positive contrapositive would be redundant.

jjinva

Posts: 65
Joined: Tue Oct 27, 2009 4:55 pm

### Re: generic question about contrapositives

So, super-comic geniuses....what is the contrapoz of a NEITHER NOR rule? Or an EITHER OR rule.

The Pen Is Mightier

Posts: 140
Joined: Fri Oct 16, 2009 1:18 pm

### Re: generic question about contrapositives

Oh how quickly lsat material leaves us!

aristotle1776

Posts: 31
Joined: Mon May 25, 2009 4:42 pm

### Re: generic question about contrapositives

So, super-comic geniuses....what is the contrapoz of a NEITHER NOR rule? Or an EITHER OR rule.

"Neither X Nor Y" is the same thing as saying 'Not X and not Y"

p -> ~y nor ~x = p -> ~y and ~x

This is a case where the English language masks the logical operation that truly connects y and x. Negated disjunctions are logically equivalent to affirmative conjunctions.

Since you change the operation when performing the contrapositive:

y or x -> ~p

With neither nors, it is probably better to just diagram the contrapositive. It is keeping in the spirit of diagramming your rules in the affirmative and is also more likely to be applicable to the game (i.e. you can quickly deduce the presence of y or x or both negates any possibility of p's presence) - useful in unbalanced games.

"Either or" depends, if the rule simply states 'either or' then we have the following rule and contrapositive:

p -> y or x
~x and ~y -> ~p

"Either or" can get tricky if they throw in an "either or, but not both" somewhere in the antecedent or consequent (usually in the consequent, if in a conditional at all). Once you practice games enough, it may become easier to keep that negation in your mind instead of taking the time to symbolize the entire thing - I found that it saves time. Eventually you will have the "situational awareness" to maybe do the same, but until then you're probably better off diagramming it.

tomwatts

Posts: 1710
Joined: Wed Sep 16, 2009 12:01 am

### Re: generic question about contrapositives

I will say, I handle the "but not both" differently every time it shows up. I'm not totally comfortable with this (seems inconsistent), but that's what I do.

For "if and only if," you get an arrow that points both ways. So...

A if and only if B
A <-> B

For the contrapositive, you could flip and negate, but the arrow points both ways, so it doesn't matter whether you flip or not.

~B <-> ~A
~A <-> ~B

Those are the same.