Just relate it with proper subset concept of set theory
suppose, set A ={1,2,3,4}
Its proper subset is any subset of A that contains atleast 1 element less than A, that means A is not a proper subset of itself.
but as empty set (phi) $\Phi$ is a subset of A that has atleast 1 element less than A so it is also a proper subset of A.
infact in general the empty set (phi) is a proper subset of every set except for the empty set, and no set is a proper subset of itself.
Similarly, if String S= “abcd” then,
empty string epsilon($\epsilon$) is also one of its prefixes.
So its prefixes are $\epsilon$, a , ab, abc , abcd
but since option b talks about proper prefix, then abcd is not considered, because
“A proper prefix of a string is a prefix that is not equal to the string itself”.
hence proper prefixes are $\epsilon$ , a , ab , abc
Thus for a ‘n’ length string, the number of proper prefixes = n.
