Confirmation of an answer of a question on Boolean Algebra

Question

Here are the solution I have worked out. Is it correct?

Given $C + BC'$:

1. $C + B' + C'$
2. $C + (B'+C')'$
3. $C + B + C$
4. $C (C + B + C)$.

Is the answer (2)?

Answer 1

$$Given: C + B\overline C = C (1 + B) + B\overline C = C + BC + B\overline C = C + B (C + \overline C) = B + C$$ $$1.\ C + \overline B + \overline C = \overline B + (C + \overline C) = \overline B + 1 = 1$$ $$2.\ C + \overline {(\overline B + \overline C)} = C + BC = C (1 + B) = C$$ $$3.\ C + B + C = B + C$$ $$4.\ C (C + B + C) = CC + BC + CC = C + BC + C = C (1 + B + 1) = C$$

Reduce them all and the answer has to be 3.

Laws and Theorems of Boolean Algebra