Which of these are partitions of the set Z x Z of ordered

Chapter 8, Problem 8.5.45

(choose chapter or problem)

Which of these are partitions of the set Z x 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 I x and 3 I y; the set of pairs (x , y), where 3 I x and 3 y y; the set of pairs (x , y), where 3 y x and 3 I y; and the set of pairs (x, y), where 3 y x and 3 y 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 :'S 0; the set of pairs (x , y), where x :'S 0 and y > 0; and the set of pairs (x , y), where x :'S 0 and y :'S 0 t) the set of pairs (x , y), where x =1= 0 and y =1= 0; the set of pairs (x, y), where x = 0 and y =1= 0; and the set of pairs (x , y), where x =1= 0 and y = 0