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

Solution

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)))