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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 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.

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.

wishyfishy wrote: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.

wishyfishy wrote: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

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