Convert function with only AND Boolean operations

Question

I have some function like ``` (A and ( B or c)) or (D and E and (F or H or R or P ))) ``` and I want to convert that function to function with only and operations (of course if possible) I find that with DeMorgan's Laws can be done some kind of transformations but I didn't manage to conver this function any ideas ? I know that function ``` !(A or B) is equal to function !A and !B ``` but I could not find the equal function to the one above

Accepted Answer

The function you mentioned:

```
!(A or B) = !A and !B
```

is the same as:

```
A or B = !(!A and !B)
```

So let's start by splitting your problem into two parts of ABC and DEFHRP.

```
(A and (B or C)) = (A and !(!B and !C))
(D and E and (F or H or R or P)) = (D and E and !(!F and !H and !R and !P))
```

Since these two parts are joined by an 'or', we can apply the equivalence again to get:

```
!(!(A and !(!B and !C)) and !(D and E and !(!F and !H and !R and !P)))
```

Convert function with only AND Boolean operations

Solution

Problem