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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- April 28th 2007, 07:29 PMJudisubset
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 - April 28th 2007, 07:32 PMThePerfectHacker
Hint: Use de Morgan's Law.

- April 28th 2007, 11:46 PMCaptainBlack
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