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

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FloridaCoastalorbust

Posts: 1356
Joined: Mon Feb 21, 2011 4:43 pm

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

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]

Jeffort

Posts: 1888
Joined: Wed Jun 18, 2008 4:43 pm

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

I'm experiencing deja vu!

cubswin

Posts: 617
Joined: Mon May 25, 2009 4:40 pm

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

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

homestyle28

Posts: 2362
Joined: Thu Jun 04, 2009 12:48 pm

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

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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