Difference between "can't both be selected" & "but not both"

[hnadgauda]

I do not understand the difference between these two statements and their conditional logic diagrams:

1. Either O or N is selected, but not both

O<-->~N
N<-->~O


2. J and K cannot both be selected

J-->~K
K-->~J

Can you please explain the difference between the two?

[ohthatpatrick]

Sure, the difference between the two is that for the 1st rule

1. Either O or N is selected, but not both

One will be IN, one will OUT, always.

For the 2nd rule

2. J and K cannot both be selected

They can both be OUT.

The 2nd rule only places a limitation on the IN column. They CAN'T both be IN.
The 1st rule places a limitation on both columns. You MUST have one of them IN and the other one OUT.

In addition to the two different ways you diagrammed the conditionals (correctly), you could also deal with them differently in terms of adding Placeholders to your master diagram.

1. Either O or N is selected, but not both

I would put a O/N in the IN column and an N/O in the OUT column of my master diagram.

2. J and K cannot both be selected

I would put a J/K+ in the OUT column.

The logic of that second one is that whenever we say
J and K can't both be IN = At least one of them is OUT

We put the little "+" next to the placeholder (optionally) to remind ourselves that they can BOTH be out. The placeholder is just saying "You're gonna have to reserve at least one spot for J/K in the OUT column, because they'll never both be IN."