How to diagram UNLESS conditional logic

emilycyoung1

How do you diagram unless, except, only if, and if but only if?

Especially unless, I'm super confused. I have been told to negate the left statement but then others say that's wrong. Also what are you supposed to do with statements like: Unless I get an A, I will not go out tonight....? HELP I HATE CONDITIONAL LOGIC

Cant Get Right

So it kind of depends on who you ask, but the end result is the same. So for “unless,” 7Sage teaches to negate the sufficient. So, “Unless A, B” would be /A —> B. But it doesn’t matter whether you make A or B the sufficient. By throwing B into the sufficient you just get: /B —> A, which is of course the contrapositive of the first statement.

I know Powerscore teaches it differently. I forget what they say, but I know they specify which term goes in the sufficient. It’s an arguably simplified, but certainly less versatile, version of the same thing.

I think the main thing is to pick one method and stick with it. It’ll definitely get confusing trying to learn it with inconsistent approaches.

emilycyoung1

@"Cant Get Right" So for my example: Unless I get an A, I will not go out tonight, do I change it to: If I don't get an A, then I don't go out tonight?

Also if it said: I won't get an A, unless I stay in tonight.

So then I would diagram: If I get an A, then I stayed in.

Is this all correct? I should have asked instead of diagramming how to produce an if then statement because I know how to diagram once i have an if then statement

Cant Get Right

@emilycyoung1 said:
Unless I get an A, I will not go out tonight, do I change it to: If I don't get an A, then I don't go out tonight?

Yep. Conversely, you could have thrown going out tonight into the sufficient: If I go out tonight, then I get an A.

@emilycyoung1 said:
Also if it said: I won't get an A, unless I stay in tonight.

So then I would diagram: If I get an A, then I stayed in.

Correct. And, of course, the other way around would result in the contrapositive: If I don’t stay in tonight, then I won’t get an A.

emilycyoung1

@"Cant Get Right" How would you diagram an except statement?

Cant Get Right

I’m trying to think of an example and I keep forming “except when” statements. So here, I really see the “when” as the logical indicator with “except” modifying it. If you’ve got an example of “except” as a lone indicator, let me know and I’ll think on it. So for an “except when” statement, let’s use:

Except when it’s humid, it’s not hot outside.

So if that were just a “when” statement, it would look like: Humid —> /Hot.
The “except” just works as a negation, so: /Humid —> /Hot.

So I kind of read the “except when” just like I do an “unless” or a “without."

legal_name

@emilycyoung1

"except" should be similar to "unless" implying that you would treat it the same way as explained above (negate sufficient). I don't believe it's specified in the curriculum though, so I would love some back-up on this in case I'm wrong. You should try to stick to words that are identified as logical indicators for now.

To answer your earlier questions:

"If (but/and) only if" translates as a bi-conditional. We usually see these come up in logic games rules. In other words, each term in the statement is sufficient for the other.

"Only if" implies necessity. So whatever statement precedes "only if" is sufficient.

Nanchito-1-1

https://7sage.com/lesson/except/

Cant Get Right

Nice find @nanchito ! I think my key take away from that was: “I think there are actually some sort of logical issues with this exact formulation of the sentence, and I don’t know if this actually translates as neatly into logic as all the rest of them.” Ha, take that “logic!" JY even says in the video he’s not entirely sure. The example used in the video certainly creates a biconditional situation, so I’m reading back up to my example and I’m honestly not sure if it’s biconditional or not. I’m kind of able to read it both ways.

LSAT tends to stay away from this kind of thing, so I wouldn’t worry too much about it. It definitely raises some interesting questions though. Would be curious to see what some others think.

quinnxzhang

@"Cant Get Right" "Except" is not always a biconditional.

Consider: No apples except red ones are edible. This expresses something like "apple & edible → red". However this does *not* mean "red → apple & edible". After all, firetrucks are also red.

Here are some academic sources that support this: http://home.uchicago.edu/~ck0/classes/nu/C72/W99/translations.html and http://legacy.earlham.edu/~peters/courses/log/transtip.htm

Cant Get Right

Thanks @quinnxzhang , I knew you’d know!