Answer
a) If the departments share the equipment, then the maximum number of each type is all that is required, so
we want to take the union of the multisets, A ∪ B.
b) Both departments will use the minimum number of each type, so we want to take the intersection of the
multisets, A ∩ B.
c) This will be the difference B − A of the multisets.
d) If no sharing is allowed, then the university needs to purchase a quantity of each type of equipment that
is the sum of the quantities used by the departments; this is the sum of the multisets, A + B.
Work Step by Step
a) If the departments share the equipment, then the maximum number of each type is all that is required, so
we want to take the union of the multisets, A ∪ B.
b) Both departments will use the minimum number of each type, so we want to take the intersection of the
multisets, A ∩ B.
c) This will be the difference B − A of the multisets.
d) If no sharing is allowed, then the university needs to purchase a quantity of each type of equipment that
is the sum of the quantities used by the departments; this is the sum of the multisets, A + B.
