islower() for strings - Python -

i doing python self-study (very beginner) , stumped on exercise i've been given - meant check if string has lower case letters:

def is_lower(word):     x in word:         if x.islower():             return true         else:             return false 

is_lower("cat") returns false

is_lower("cat") returns true

and is_lower("cat") returns true

i'm not sure why getting these differences - appears testing first letter of word, , i'm not sure why. thought should iterating through each letter of word, since loop

you need keep looping until read characters.

for x in word:     if x.islower():         # found *one* lower case letter, return true         return true # found *no* lower case letters, return false return false 

or, can simplify:

return any(x.islower() x in word)