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Math Help - subset

  1. #1
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    subset

    Let A, B, C be subset of Z^2 where A=((x,y)ly=2x+1) B=((x,y)ly=3x) and
    C=((x,y)lx-y=7)
    Determine (compliment of B) U (compliment of C)?
    answer is Z^2 and why is that?

    I thank you everyone in advance,
    Judi
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  2. #2
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    Quote Originally Posted by Judi View Post
    Let A, B, C be subset of Z^2 where A=((x,y)ly=2x+1) B=((x,y)ly=3x) and
    C=((x,y)lx-y=7)
    Determine (compliment of B) U (compliment of C)?
    answer is Z^2 and why is that?

    I thank you everyone in advance,
    Judi
    Hint: Use de Morgan's Law.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Judi View Post
    Let A, B, C be subset of Z^2 where A=((x,y)ly=2x+1) B=((x,y)ly=3x) and
    C=((x,y)lx-y=7)
    Determine (compliment of B) U (compliment of C)?
    answer is Z^2 and why is that?

    I thank you everyone in advance,
    Judi
    Consider a point (x,y) in Z^2 in both B and C. Then y=3x, and x-y=7, so:

    -2x = 7

    but the lefthand side is even and the right hand side is odd, which is
    impossible so B intersection C = null set.

    But (by De Morgan's laws):

    complement(B intersection C) = (compliment B) U (compliment C),

    and as compliment(null set) = Z^2, we have:

    (compliment B) U (compliment C) = Z^2.

    RonL
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