1. a) Doll's house is very nice. OR b) The doll's house is nice. (Are both correct?)
2. a) Andres' cellphone has some scratches on the screen. OR b) The Andres' cellphone has some scratches on the screen. (Are both correct?)
3. a) Green's house on the Mejia street is my favorite. OR b) The green's house on the Mejia street is my favorite. (Are both correct?)
4. a) A friend's University is so big. OR b) A friend's University is so big. (Are both correct?)
1- Both are correct with different meanings:
a) Doll's house:The house which is belonged to a person whose name is Doll.
b) The doll's house: 1st meaning: The house which is belonged to the doll's family. 2nd meaning: The house which is belonged to a toy.
2- The first in not common. Use "the" before objects.
3- If you mean green color, None of them is correct-> The green house.
"The Green's house" means a house which is belonged to the Green's family.
4- u have written same sentences.
Good Luck Dear Soffy
