# How to represent subset using 5-bit binary code?

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?

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.