Let $B = \{1, 2, 3, 6, 12, 18\}$ and $R$ be defined by $xRy$ if and only if $x|y$.
a) Determine all minimal and all maximal elements of the poset.
b) Find all least and greatest elements of the poset.
I am most confused about minimal, but here is what I have for an explanation and an answer. Am I on the right track?
MAXIMAL: Cannot be made to divide a bigger number; it is not less than another element. Answer: $12$ and $18$
MINIMAL: Can be made to divide a bigger number; it is less than another element. Answer: $1$
GREATEST: One number that every other element divides into. Answer: There is no one single number.
LEAST: One number that divides into every other element. Answer: $1$