Given a word, treat every letter as it's number in English alphabet (so
a becomes 1,
b becomes 2,
z becomes 26 and so on), and check if all of them, including duplicates, are pairwise coprime.
The input is exactly one word of lowercase English letters. The output is the fact if the word is coprime: any truthy/falsey values, but only two variants of them. Standard loopholes are forbidden.
True(thanks to Ørjan Johansen)
aoccurs multiple times, 1 and 1 are coprimes)
False(thanks to xnor; though
True(if no pairs of letters, treat the word as coprime too)
This is a code-golf, so the shortest code in bytes wins!