x(y + 1)

Question

dual of x(y + 1)

Answer 1

x(y+1)=x.(y+1) (same as x AND (y OR 1) where x and y are Booleans).

Note that y+1=y OR 1=1.

y OR 1 has the dual y AND 0=0. And 0 is the dual of 1, so x OR (y AND 0)=x OR 0=x.

The dual of x(y+1) is x.

Another way of interpreting x(y+1) is to consider TRUE and FALSE. 1 means TRUE. If we have two statements and one is known to be TRUE then it's also TRUE that either one or the other is TRUE. And the dual of TRUE is FALSE. So we now have x OR FALSE that is, if x is FALSE then we can say that either one or the other is FALSE. If x is TRUE we can say that either one or the other is TRUE. So the TRUE/FALSE state of x alone determines the result.