How to represent subset using 5-bit binary code?

Question

For the set $V=\{a, e, i, o, u\}$, give the $5$-bit binary string that codes each of the following subsets: $\{a, i,o\}; \{e\}; V; \emptyset$;

Which subset is represented by the $5$-bit string $10001$?

Can I know how do you get the 5-bit binary string from the respective subsets? What are the differences between using 3-bit binary string to represent them and using 5-bit binary string?

Answer 1

The code $10001$ would represent $\{a, u\}$. More generally, if you have a sequence $a_1, a_2, a_3, a_4, a_5$, you can code any subsequence by a $5$-bit string, with the convention that the $i$-th bit of your string is set to $1$ if and only if $a_i$ appears in the subsequence.