# Regular expression for strings not starting with 10

How can I construct a regular expression for the language over $$\{0,1\}$$ which is the complement of the language represented by the regular expression $$10(0+1)^*$$?

If a word doesn't start with $$10$$, then either it starts with some other combination of two letters, or it is shorter than two letters. All in all, we get the following regular expression for your language: $$\epsilon + 0 + 1 + (00+01+11)(0+1)^*.$$
• I must admit I'm not very familiar with this style of regular expressions, but couldn't you say e+1+(0+11)(0+1)*? Dec 7 '19 at 23:39