Mapping conditional reasoning on LG Forum

[77to101]

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]

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]

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

[aether]

what do the vs represent?

v is the old-fashioned logic symbol for OR.

[77to101]

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?