blue trane's Journal: logical unless

"Unless you do your homework, you can't go out"

A guy in #philosophy wanted to interpret this as an equivalence relation, or bidirectional implication. I wanted to interpret it as simple implication. Then it struck me, the sentence could be part of two truth tables:

Let A = "do homework"
Let B = "go out"

A.........B.........->
---------------------------
T.........T.........T
T.........F.........F
F.........T.........T
F.........F.........T

not-A..not-B....->
------------------------------
T.........T.........T
T.........F.........F
F.........T.........T
F.........F.........T

The sentence "Unless you do your homework, you can't go out" could be either the last line in the first truth table, or the first line in the second truth table.

To determine which one it is, you can ask: If you do your homework and can't go out, then you're in the second truth table.
If you don't do your homework but can go out, then you're using the first truth table.

To make a bidirectional relation, you could change "can't go out" to "don't have the possibility of going out". Then both of the middle lines become false and the statement is only true if you do your homework and have the possibility of going out, or if you don't do your homework and don't have the possibility of going out.