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Homework Help: Boolean Alegebra

  1. Feb 20, 2008 #1
    if [tex]A \oplus B=C[/tex], then [tex]C \oplus B=A[/tex], and [tex]A \oplus C=B[/tex] (use substitution)

    [tex]C \oplus B=A[/tex]

    [tex]C \overline{B} + \overline{C} B = A[/tex]

    [tex](A \oplus B) \overline{B} + (\overline {A \oplus B}) B = A[/tex]

    [tex](A \overline{B} + \overline {A} B ) \overline {B} + (AB+ \overline{A} \overline{B})B=A[/tex]

    [tex]A \overline{B} \overline {B} + \overline {A} B \overline{B} + ABB + \overline{A} \overline{B}B=A[/tex]

    [tex]AB + 0 + AB + 0 = A[/tex]

    AB = A

    I don't know how to get A = A

    Any help?
     
    Last edited: Feb 20, 2008
  2. jcsd
  3. Feb 20, 2008 #2
    Am I doing the steps correctly?
     
  4. Feb 21, 2008 #3
    Anybody know how to solve
     
  5. Feb 21, 2008 #4

    CEL

    User Avatar

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

    [tex]A(\overline{B} + B) = A[/tex]

    [tex]A.1 = A[/tex]

    [tex]A = A[/tex]
     
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