All the definitions I came across so far stated, that if a statement is true, then also its dual statement is true and this dual statement is obtained by changing `+` for `.`, `0` for `1` and vice versa.

However when I say `1+1`, whose dual statement according to the above is `0.0`, I get opposite results, that is:

```
1 + 1 = 1
0 . 0 = 0

```

How should I understand this duality principle ?