Question

Let

X = {5, 10, 15, 20, 25, 30, 35, 40}.
Define a relation

on X as follows. For
a, b is in X,

a

b
if b can be obtained from a by adding a (possibly empty) collection of dimes (10 cents) and quarters (25 cents). So, for example,
25

35, but 25

30.


List all minimal elements of
(X,

).
(Enter your answers as a comma-separated list.)

Answer 1

Here is the answer in comma-separated list.

(5, 10) , (10,15), (15, 20) (20, 25) (25, 300 (30, 35)

You need 5 dimes while having 10 or 25