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.
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