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

Quote:

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Originally Posted by Judi

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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Hint: Use de Morgan's Law.

Quote:

---

Originally Posted by Judi

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