Which of these collections of subsets are partitions of the
set of integers?

a) the set of even integers and the set of odd integers

b) the set of positive integers and the set of negative integers

c) the set of integers divisible by 3, the set of integers
leaving a remainder of 1 when divided by 3, and the
set of integers leaving a remainder of 2 when divided
by 3

d) the set of integers less than −100, the set of integers
with absolute value not exceeding 100, and the set of
integers greater than 100

e) the set of integers not divisible by 3, the set of even
integers, and the set of integers that leave a remainder
of 3 when divided by 6