I have a problem (A+B)(A+C)(A+D)=A+BCD. I'm a litte rusty on my two-state logical signals and was wondering if someone could push me in the right direction so i can prove this relation.

 

(a+b)(a+c)(a+d)=aaa+aac+aab+abc+aad+acd+abd+bcd
= A + Ac + Ab + Abc + Ad + Acd + Abc + Bcd (because A.a=1)
= A(1 + C + B + Bc + D + Cd + Bc ) + Bcd (because 1 + Anything = 1)
= A + BCD