Some Logic

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.