Let Z be the set of all integers and let {n € Z]n = 4k, for some integer k} {n € Z]n = 4k + 1, for some integer k} A2 {n €Z]n = 4k + 2, for some integer k} and Az = {n € Z |n = 4k + 3, for some integer k}. s{Ao•Ag Az, Ag a partition of Z? Why or why not? O Yes. Z = A, U A1 U A, U A3, and A, n Az = Ø, A, N A2 = Ø, A, N Az = Ø, A N Az = Ø, A, N A3 = Ø, A, N Az = Ø. O Yes. Z = A, nA, N A, N A3, and A, U A, = Ø, A, U A, = Ø, A, U A3 = Ø, A, U A2 = Ø, A, U A3 = 0, A2 U A, = Ø. O No. Z + A, U A, U A, U A, and A, NA, # Ø. O No. Z = A, n A, N but A, U A, # Ø. O No. Z = A, U A, UA, U A3, but A, N A, # Ø.

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