(a) Each of the following true statements contains an implication. (i) For all a, b ∈ Z, if a − b is even then a + b is even. (ii) For all A ⊆ N, if A is finite then Ac is infinite. Write down the...

(a) Each of the following true statements contains an implication.
(i) For all a, b ∈ Z, if a − b is even then a + b is even.
(ii) For all A ⊆ N, if A is finite then Ac
is infinite.
Write down the converse of each statement and decide (with justification) whether it is true or false.
(b) Consider the statement: For all x, y, z ∈ Z. At least one of x− y, x− z
and y − z is even.
(i) Write down a roadmap for a proof of this statement by contradiction.
(ii) Fill in the details of your roadmap to prove the statement.