Tricky contrapositive? PT 33, S4 (LG) Game 2.

FloridaCoastalorbust
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Joined: Mon Feb 21, 2011 4:43 pm

Tricky contrapositive? PT 33, S4 (LG) Game 2.

Postby FloridaCoastalorbust » Mon Apr 18, 2011 4:17 pm

PT 33, S4 (LG) Game 2. Here is the rule:

If jays, martins, or both are in the forest, then so are harriers.

I've come across this several other times and always waste a few seconds trying to get the perfect representation, and have been confused about the contrapositive. Anyone want to shed some light? Today, I diagrammed as follows

(J or M) or (J and M) --> H

Contrapositive:

~H --> ~J and ~M [or ~H --> ~(J or M) for all you DeMorgan's Law lovers]

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Jeffort
Posts: 1896
Joined: Wed Jun 18, 2008 4:43 pm

Re: Tricky contrapositive? PT 33, S4 (LG) Game 2.

Postby Jeffort » Mon Apr 18, 2011 4:22 pm

I'm experiencing deja vu!

cubswin
Posts: 618
Joined: Mon May 25, 2009 4:40 pm

Re: Tricky contrapositive? PT 33, S4 (LG) Game 2.

Postby cubswin » Mon Apr 18, 2011 4:29 pm

Bro,

J or M already includes the possibility of J and M. They just wrote it that way to be dicks. You only need to symbolize it like this:

J or M --> H
~H --> ~J and ~M

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homestyle28
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Re: Tricky contrapositive? PT 33, S4 (LG) Game 2.

Postby homestyle28 » Mon Apr 18, 2011 4:30 pm

FloridaCoastalorbust wrote:PT 33, S4 (LG) Game 2. Here is the rule:

If jays, martins, or both are in the forest, then so are harriers.

I've come across this several other times and always waste a few seconds trying to get the perfect representation, and have been confused about the contrapositive. Anyone want to shed some light? Today, I diagrammed as follows

(J or M) or (J and M) --> H

Contrapositive:

~H --> ~J and ~M [or ~H --> ~(J or M) for all you DeMorgan's Law lovers]


Strictly speaking the 2nd part of your disjunction is redundant. The simplest way is (J v M) -> H :: ~ H -> ~(JvM)/ ~J and ~M.




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