Recently on #logic via twitter Pete Lewis asked:-
a || b -> !(!a || !b)) ? #logic makes my brain hurt
I did a quick truth table on paper and said yes but turns out I was wrong as I had looked at the wrong columns. Doh! Here’s the truth table and you can see for yourself
| A | B | A || B | !A | !B | (!A || !B) | !(!A || !B) |
| FALSE | FALSE | FALSE | TRUE | TRUE | TRUE | FALSE |
| FALSE | TRUE | TRUE | TRUE | FALSE | TRUE | FALSE |
| TRUE | FALSE | TRUE | FALSE | TRUE | TRUE | FALSE |
| TRUE | TRUE | TRUE | FALSE | FALSE | FALSE | TRUE |
The colums A || B and !(!A || !B) are not equivalent.
