Let O = {x Z | x is odd} be the set of odd integers and E = {x Z | x is even} be the set of even integers. (a) Explain whether {O, E} is a partition...

Let O = {x ∈ Z | x is odd} be the set of odd integers and E = {x ∈ Z | x is even} be the set of even integers. (a) Explain whether {O, E} is a partition of Z. (b) Explain whether {O × O, E × E} is a partition of Z × Z. If the answer is no for either question, can you extend the collection so that it becomes a partition of the given set.