I read some books talk about RSA cryptography but I did not understand something when choosing a public key $e$ Sometimes the condition is
$1<e<$$\phi(n)$
Where $\phi(n) = p-1 * q-1$
also sometimes is
$e \in [{1,2,...,\phi(n)-1}]$
also sometimes is
$e$ should be prime number
Examble
Choose $p = 3\ and\ q = 11 $
Compute $n = p * q = 3 * 11 = 33 $
Compute $\phi(n) = (p - 1) * (q - 1) = 2 * 10 = 20$
Choose $e$ .here can choose e = 7 where 7 is prime number or I can choose $e=9$ where 9 is relatively prime to 20.
My question
Are both states right when choose 7 and 9. or not right .If no why???