Boolean Simplification  Why does (A + NOT(B.C)).(B + NOT(B.C)).(C + NOT(B.C)) = A + NOT B.C
This is the answer to the equation, but I do not understand why. Please help!
1 answer

If you apply the Laws of Boolean Algebra one by one, the solution is a direct result:
 de MorganĀ“s Theorem: The complement of two terms joined together by
OR
is the same as the complements of two terms joined byAND
, and vice versa (i.e.NOT(A + B) = NOT(A) * NOT(B)
andNOT(A * B) = NOT(A) + NOT(B)
).  Commutative Law: The order of joining two separate terms with
AND
orOR
is not important.  Complement Law: A term joined with its complement with
AND
equals0
respectively withOR
equals1
(i.e.A * NOT(A) = 0
andA + NOT(A) = 1
).  Annulment Law: A term joined with
AND
with0
equals0
and joined withOR
with a1
equals1
(i.e.A * 0 = 0
andA + 1 = 1
).  Identity Law: A term joined with
1
byAND
or with0
byOR
is equal to itself (i.e.A * 1 = A
andA + 0 = A
).
(there are more, but you don't need them here)
Applied to your term:
(A + NOT(B*C)) * (B + NOT(B*C)) * (C + NOT(B*C)) [with 1.] = (A + NOT(B) + NOT(C)) * (B + NOT(B) + NOT(C)) * (C + NOT(B) + NOT(C)) [with 2.] = (A + NOT(B) + NOT(C)) * (B + NOT(B) + NOT(C)) * (C + NOT(C) + NOT(B)) [with 3.] = (A + NOT(B) + NOT(C)) * (1 + NOT(C)) * (1 + NOT(B)) [with 4.] = (A + NOT(B) + NOT(C)) * 1 * 1 [with 5.] = (A + NOT(B) + NOT(C)) [with 1.] = (A + NOT(B*C))
 de MorganĀ“s Theorem: The complement of two terms joined together by