Regular Expressions

Question

$L_1=\{a^nb^m\mid n\geq 3,m\leq 4\}$

Find complement of $L_1.$

Answer 1

Given language L=aⁿb^m/ n>=3 and m<=4, i.e- L contain all the strings that have Num of a>=3 followed by num. of b<=4. Eg- aaaaabb.
Complement of a language contains all strings that are not in the given language.
So Complement of L contains:
1.    Strings starting with b i.e  b(a*b*)* or
2.    { aⁿb^m | n<3 or m>4}  
So,  L1=  b(a*b*)* U { aⁿb^m/ n<3 or m>4}  

Answer 2

aⁿ b^m  / n <= 3,m>=4 this is  L₁ Compliment i think so