Question

Prove the following using the properties of regular expressions:

1. (ab)* + c + c* = Λ + ab + (ab)* + c(Λ + c*)  
2. Λ+ab+abab+ababab(ab)* = Λ + ∅* + (ab)*
3. a(b+c*) + (d+e)* = ab + ac*c* + d + e + (d+e)*
4. a*b + a*a*bc* + d* + ab = d* + ab + a*bc* + Λ
5. a(b+cd*) = a(b+c) + acdd*
6. (a+b)* = ∧* + ∅* + (a*b*)*
7. (ab)*(c*+d*) = (ab)*(c+c*) + (ab)*( ∧ + d*)
   

Answer 1