# Boolean Alegebra

1. Feb 20, 2008

### needhelp83

if $$A \oplus B=C$$, then $$C \oplus B=A$$, and $$A \oplus C=B$$ (use substitution)

$$C \oplus B=A$$

$$C \overline{B} + \overline{C} B = A$$

$$(A \oplus B) \overline{B} + (\overline {A \oplus B}) B = A$$

$$(A \overline{B} + \overline {A} B ) \overline {B} + (AB+ \overline{A} \overline{B})B=A$$

$$A \overline{B} \overline {B} + \overline {A} B \overline{B} + ABB + \overline{A} \overline{B}B=A$$

$$AB + 0 + AB + 0 = A$$

AB = A

I don't know how to get A = A

Any help?

Last edited: Feb 20, 2008
2. Feb 20, 2008

### needhelp83

Am I doing the steps correctly?

3. Feb 21, 2008

### needhelp83

Anybody know how to solve

4. Feb 21, 2008

### CEL

You made a mistake in line 6. You should have:
$$A\overline{B} + 0 + AB + 0 = A$$

$$A(\overline{B} + B) = A$$

$$A.1 = A$$

$$A = A$$