I have the following function to be reduced/simplified.

F(A,B,C,D) = BC + (A + C'D') where ' denotes the complement

```
Here's my solution:
= BC + (A + C'D')'
= BC + (A + (C+D)
= BC + (A + C + D)
= BC + C + A + D
= C(B + 1) + A + D
= C*1 + A + D
= C + A + D
```

Is this correct?

### Answer1:

As in traditional algebra, if you do something to one side of the equation, you must do it to the other side, including complementing. Here we state the original equation:

F'(A,B,C,D) = BC + (A + (CD)')

Since we have F' instead of F, my intuition tells me to complement both sides, but first I distribute the complement in the term (CD)' to make life easier in the long run:

F' = BC + (A + (C'+ D'))

Now we can complement both sides of the equation:

1: F = '(BC)'(A + (C'+ D')) The OR becomes AND after distributing complement

Now let's distribute the complements inside just to see what we get:

2: F = (B'+ C')(A'(CD))

Now we can just distribute the right term (A'(CD)) over the two terms being OR'ed:

3: F = B' *(A'(CD))* + C' *(A'(CD))*

We see that the right term goes away since we have a CC' and thus we are left with:

4: F = A'B'CD

Hopefully I didn't make a mistake. I know you've found the answer, but others reading this might have a similar question and so I did it out to save duplicate questions from being asked. Good Luck!

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