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## Homework Statement

Use only DeMorgan's relationships and Involution to find the complements of the following functions:

a.) f(A,B,C,D) = [A+(BCD)'][(AD)'+B(C'+A)]

## Homework Equations

Demorgans (x

_{1}+ x

_{2}+ ... + x

_{n})' = x

_{1}'x

_{2}'...x

_{n}'

Involution (x')' = x

## The Attempt at a Solution

[[A+(BCD)'][(AD)'+B(C'+A)]]' to find the compliment, then using demorgans

[A+(BCD)']' + [(AD)'+B(C'+A)]'

[A'(BCD)] + (AD)[B(C'+A)]'

A'BCD + (AD)[B' + (C'+A)']

A'BCD + (AD)(B' + CA')

from here I don't know where to go, i would think the right side of the equation could turn to ADB' + ADCA' but I'm not sure, if it can ADCA' would just be 0 since AA' = 0. Don't know if I can do that though, just looking for some input and hopefully I didn't make a mistake towards the begining.

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