## Mapping conditional reasoning on LG

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77to101

Posts: 22
Joined: Wed Sep 23, 2009 2:53 am

### Mapping conditional reasoning on LG

How would you map these constraints and their contrapositives?
If Y is not selected, then either L or O, but not both, are selected.
If it is not the case that the group selected includes both L and O, then it contains F and S.

Thanks!

BenJ

Posts: 1336
Joined: Mon Dec 28, 2009 12:58 pm

### Re: Mapping conditional reasoning on LG

The first:
~Y -> (L v O) & ~(L & O)
L & O -> Y
~L & ~O -> Y

Separating the contrapositive makes it easier to read.

The second:
~L v ~O -> F & S
~F v ~S -> L & O

77to101

Posts: 22
Joined: Wed Sep 23, 2009 2:53 am

### Re: Mapping conditional reasoning on LG

thank you. what do the vs represent? also, can you write out the contrapositives in words?

aether

Posts: 57
Joined: Wed Dec 09, 2009 12:25 am

### Re: Mapping conditional reasoning on LG

77to101 wrote:what do the vs represent?

v is the old-fashioned logic symbol for OR.

77to101

Posts: 22
Joined: Wed Sep 23, 2009 2:53 am

### Re: Mapping conditional reasoning on LG

aha! So that's what was tricky.
I wasn't sure how to diagram the "but not both" part of the first constraint "If Y is not selected, then either L or O, but not both, are selected." Without the "but not both", it'd be a simple "~Y -> L or O" with its contrapositive "~L and ~O ->Y", right? So for the "but not both" part, the trick is to treat the "L and O" as one block, so that it's "~Y->(LandO)" with its contrapositive "~(LandO)->Y", as opposed to the "~Y->L and O" and its contrapositive "~L or ~O ->Y" that I was thinking of originally.
Is my thought process now correct?