Question: Which of these are partitions of the set Z × Z of ordered pairs of integers?
a) the set of pairs (x, y), where x or y is odd; the set of pairs (x, y), where x is even; and the set of pairs (x, y), where y is even
b) the set of pairs (x, y), where both x and y are odd; the set of pairs (x, y), where exactly one of x and y is odd; and the set of pairs (x, y), where both x and y are even
c) the set of pairs (x, y), where x is positive; the set of pairs (x, y), where y is positive; and the set of pairs (x, y), where both x and y are negative
d) the set of pairs (x, y), where 3 | x and 3 | y; the set of pairs (x, y), where 3 | x and 3 | y; the set of pairs (x, y), where 3 | x and 3 | y; and the set of pairs (x, y), where 3 | x and 3 | y
e) the set of pairs (x, y), where x > 0 and y > 0; the set of pairs (x, y), where x > 0 and y ≤ 0; the set of pairs (x, y), where x ≤ 0 and y > 0; and the set of pairs (x, y), where x ≤ 0 and y ≤ 0
f) the set of pairs (x, y), where x = 0 and y ≠0; the set of pairs (x, y), where x ≠0 and y ≠ 0; and the set of pairs (x, y), where x≠ 0 and y ≠ 0