Can someone please explain this LG "rule" for me?

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Can someone please explain this LG "rule" for me?

Postby notaznguy » Thu Sep 15, 2011 4:56 am

This rule was from a game in the Feb 1999 test.

The rule said, "If it is not the case that the park contains both A and B, then the park contains C and D."

I diagrammed it as:

Valid: -A and -B --> C and D
Contrapositive: -C or -D --> A or B

HOWEVER, this was totally wrong and drawing this rule wrong ultimately screwed me over for the whole game.

I found out that the rule should have been drawn out as:

Valid: -A or -B --> C and D
Contrapositive: -C or -D --> A and B

I thought when it says "It is NOT the case that there is both," it mean there must not be both A and B. There can't be both. So it is

-A and -B

Why is this not right?

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Re: Can someone please explain this LG "rule" for me?

Postby Jeffort » Thu Sep 15, 2011 7:55 am

See this thread: ... html#msg72,30.0.html

I've also posted my same/similar explanation numerous times on this board but cannot find the posts quickly.

The trees in the park game is nasty but also really tests you on the fundamentals of conditional reasoning including how multiple compound conditional rules can interact, especially in the context of an in/out selection game.

You misinterpreted the rule. If it is not the case that BOTH are selected, the valid connector is OR not AND, since not having both only requires one of the two to be absent/not selected. In that game, if you mess up that rule, the whole thing goes down the toilet and you cannot put together the transitive chains of conditional rules that makes the questions easy.

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