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Math Help - Boolean algebra problem

  1. #1
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    Boolean algebra problem

    Hello,
    I need to prove that this expression is correct (in boolean algebra) and I can't figure out how.
    WXY'Z'+XYZ+WY'Z'+WXZ=XYZ+WY'(X+Z')
    Can anyone help me?
    Thanks in advance
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  2. #2
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    Re: Boolean algebra problem

    What do you mean by a correct expression and what can you use in a proof? Can you use truth tables?
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  3. #3
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    Re: Boolean algebra problem

    I need to prove that the expression is true and I cannot use truth tables. I need manipulate the expression with rules like DeMorgen sentence for example so both sides of the expression will be equal
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  4. #4
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    Re: Boolean algebra problem

    Working on the right-hand side,
    \begin{align*}
    xyz+wy'(x+z')&= xyz+wxy'+wy'z'\\ &=xyz+wxy'(z+z')+wy'z'\\ &=xyz+wxy'z+wxy'z'+wy'z'.
    \end{align*}
    Now, working on the left-hand side,
    \begin{align*}
    wxy'z'+xyz+wy'z'+wxz &=wxy'z'+xyz+wy'z'+wx(y+y')z\\ &=wxy'z'+xyz+wy'z'+wxyz+wxy'z\\ &=wxy'z'+xyz(1+w)+wy'z'+wxy'z\\ &=wxy'z'+xyz+wy'z'+wxy'z
    \end{align*}
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  5. #5
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    Re: Boolean algebra problem

    Thank you very much!
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