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Math Help - im pretty sure this is true

  1. #1
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    im pretty sure this is true

    (A and B) U (A - C) = A -(C - B)
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  2. #2
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    Quote Originally Posted by leinadwerdna View Post
    (A and B) U (A - C) = A -(C - B)
    HI

    We will start from the LHS .

    (A n B) u (A-C)

    (A n B) u (A n C')

    A n (B u C') .... distributive

    A n (B' n C)' ..... de morgan

    A n (C n B')' .... associative

    A - (C - B)
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  3. #3
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    can you explain de Morgan's law
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by leinadwerdna View Post
    can you explain de Morgan's law
    \left[\bigcup_{i=1}^{n} U_i \right]^c=\bigcap_{i=1}^{n}U_i^c where ^c denotes the complement. An obvious corrolary of this is that \left[\bigcap_{i=1}^{n}U_i\right]^c=\left[\bigcap_{i=1}^{n}\left(U_i^c\right)^c\right]^c=\left[\left[\bigcup_{i=1}^{n}U_i^c\right]^c\right]^c=\bigcup_{i=1}^{n}U_i^c.
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  5. #5
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    Quote Originally Posted by leinadwerdna View Post
    can you explain de Morgan's law
    De morgan's law states that

    (A u B)'=A' n B'

    (A n B)'=A' u B'
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