1. Write down the converse of each statement and decide (with justification) whether it is true or false. (a) Each of the following true statements contains an implication. (i) For all a, b ∈ Z, if a...

1. Write down the converse of each statement and decide (with justification) whether it is true or false.

(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.

(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.