If not _______, then ______ Forum

[wishyfishy]

This rule, and "unless ________, then (not) ________." I've heard that it's a good to use a real life situation to figure out the inferences to rules. For example, I remember "if it rains, then I will get wet" for the "if ________, then ________" rule. That way when I reverse it and say "if I get wet," it makes sense that it's not necessarily from rain. But I can't seem to think of any examples that work for these two rules and whenever I encounter them, it takes me a good 30 seconds to figure out the inferences. So does anyone have a one sentence trick for remembering these?

[JoeFish]

If not X then Y is the same as "If ~X then Y", which is identical to "At least one of X or Y"
No X unless Y is the same as "If X then Y".
Unless Y, no X is the same as "If X then Y".

Just remember that you need the "no ___" in there for the last two. If it's X unless Y, then it's "If ~X then Y".

Although you may be looking something less logicspeak than this.

[lsatprepguy]

IIRC, when you see unless, that is the necessary condition, then negate the other part and that is the sufficient.

For example:
The dog walks unless it is raining outside.
----------------------------------------------------------------
It is raining outside becomes the necessary condition.
--> It is raining outside.

The other part, negated, becomes the sufficient condition.

The dog does not walk ---->

TOGETHER
The dog does not walk ---> It is raining outside.

[tomwatts]

So does anyone have a one sentence trick for remembering these?

Unless I have a pencil, I won't be able to do well on the LSAT. Equivalently, if I don't have a pencil, I won't be able to do well on the LSAT.

I know, it's cheesy, but this is the example that I use in class. Obviously, the pencil is necessary but not sufficient for doing well.

[EarlCat]

This rule, and "unless ________, then (not) ________." I've heard that it's a good to use a real life situation to figure out the inferences to rules. For example, I remember "if it rains, then I will get wet" for the "if ________, then ________" rule. That way when I reverse it and say "if I get wet," it makes sense that it's not necessarily from rain. But I can't seem to think of any examples that work for these two rules and whenever I encounter them, it takes me a good 30 seconds to figure out the inferences. So does anyone have a one sentence trick for remembering these?

"If not" diagrams just like "If," except with a "not" (usually represented by ! or ~)
If not A then B.
~A --> B

If you want a cute sentence, my dad used to say things like, "If they ain't bitchin' they ain't happy." Same "if not" diagram.
~B --> ~H

You can also think of "unless" as "if not."
Unless I have oxygen, I will die (or I will die unless I have oxygen).
~O --> D

[bp shinners]

Unless, until, except, and without can all be replaced with 'if not'. Significantly easier to work with.