Biconditionals and conditionals in in/out

[hyk1310]

Just to make sure I'm on the right footing for in/out games.

There are two biconditional types.

One is where both are in or both are out, like A <--> B.

The other, is where A and B simply switches places, like A<--> Not B. By switching places, I mean A is in B is out, and B is in and A is out.

Now, for simple conditionals where A--> Not B,

there could be three implications.

1. A and B are both not in.
2. A is in B is not in.
3. B is in A is not in.

Are these all the possible implications we can make from biconditionals and normal conditional statements, limited to the examples that I have given above?

Thank you!

[ohthatpatrick]

Sounded good.

Biconditionals are somewhat rare.

I would think of the two types as FRIENDS and ENEMIES (or chunks and anti-chunks). In grouping games, the most common rules are "These two guys are in the same group" (friends) and "These two guys can't be in the same group" (enemies).

I don't write either of those as conditionals. I just write them as
(AB) if it's friends, or ~(AB) if it's enemies

When it's enemies, you should be putting an A/B placeholder in each column.
When it's friends, you consider framing both IN and both OUT.

There are 3 types of conditionals:

i. can't both be IN
ii. can't both be OUT
iii. the others

i. can't both be IN
"If J is in, K is out"

can't both be IN = at least one OUT
(put a J/K placeholder in the OUT column)

ii. can't both be OUT
"If M is out, P is in."

can't both be OUT = at least one IN
(put a M/P placeholder in the IN column)

iii. The others
"If R is in, T is in."
"If T is out, R is out."

These don't come with placeholders, but they come into play as you go through the game when you only have one more spot in the IN or OUT column.

If I only have one more IN spot, then it must be T.

If I only have one more OUT spot, then it must be R.