a: Let A={1,2,3,4,5,6}, A1 = {1,2}, A2 = {3,4}, and A3= {5,6}. Is {A1, A2, A3} a partition of A?
Prove your answer.
b: Let Z be the set of all integers and let
T0 = {n ∈Z | n = 3k, for some integer k},
T1 = {n ∈Z | n = 3k + 1, for some integer k}, and
T2 = {n ∈Z | n = 3k + 2, for some integer k}.
Is {T0, T1, T2} a partition of Z? Prove your answer.

I'm not sure how to prove it...

I know the answer to number 1 is Yes, because the elements of the set cover A and the intersection between each element is the null set. Unsure on B.

Question

a: Let A={1,2,3,4,5,6}, A1 = {1,2}, A2 = {3,4}, and A3= {5,6}. Is {A1, A2, A3} a partition of A?
Prove your answer.
b: Let Z be the set of all integers and let
T0 = {n ∈Z | n = 3k, for some integer k},
T1 = {n ∈Z | n = 3k + 1, for some integer k}, and
T2 = {n ∈Z | n = 3k + 2, for some integer k}.
Is {T0, T1, T2} a partition of Z? Prove your answer.

I'm not sure how to prove it...

I know the answer to number 1 is Yes, because the elements of the set cover A and the intersection between each element is the null set. Unsure on B.