Question about deduction of reciprocal rule

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logicgamesbrah

Posts: 29
Joined: Sat Oct 09, 2010 5:21 pm

Question about deduction of reciprocal rule

In LG when you get a rule that allows you to reverse the rule without negating and it's still true what is the deduction you get from this rule?

For example in a game where you have 5 entities and four spots to place them.

If no A -> B second, contraposed as
If B not second -> A

If B second -> not A, contraposed as
If A -> B not second

What deduction can be made from this rule?

KevinP

Posts: 1322
Joined: Sat Sep 26, 2009 8:56 pm

Re: Question about deduction of reciprocal rule

logicgamesbrah wrote:In LG when you get a rule that allows you to reverse the rule without negating and it's still true what is the deduction you get from this rule?

For example in a game where you have 5 entities and four spots to place them.

If no A -> B second, contraposed as
If B not second -> A

If B second -> not A, contraposed as
If A -> B not second

What deduction can be made from this rule?

If I understand this correctly, you have the following rules
not A -> B2
B2 -> not A

There is no point to taking the contrapositive (unless it helps w/ finding the bidirectional) as it can be written as a bidirectional.
not A <--> B2
and the only time this can be true is under the following 2 conditions:
B is second and A is not included (since this is out of 5, the other 4 have to be included)
B is not second and A is included.

I hope that helps, let me know if I can be of any further help.