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

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FloridaCoastalorbust

Posts: 1350
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]

soj

Posts: 7890
Joined: Sat Jan 16, 2010 11:10 pm

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

J -> H
M -> H
~H -> ~J & ~M

Those three rules are enough to represent every situation that obeys that rule.

Now if it said (J or M but not both) -> H, then it gets interesting.

Then I think you would have to do this:
J & ~M -> H
~J & M -> H
i.e. if J and M are NOT on the same side, then H is on the IN side.
~H -> (J & M) OR (~J & ~M)
i.e. if H is not selected, then J and M have to be on the same side, whether it's on the IN side or the OUT side.
Last edited by soj on Mon Apr 18, 2011 4:23 pm, edited 1 time in total.

FloridaCoastalorbust

Posts: 1350
Joined: Mon Feb 21, 2011 4:43 pm

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

soj wrote:Don't worry about the both.

J -> H
M -> H
~H -> ~J AND ~M

thx soj