1. Emily is Rose's sister.
2. Emily is Rose' sister.
3. Mike is Alice's brother.
4. Mike is Alice' brother.
[Which ones are grammatical? It's the use of possessive case.]
Only 1 and 3 are correct.
Out of the four sentences, the grammatically correct ones are:
1. Emily is Rose's sister.
3. Mike is Alice's brother.
The possessive form of a singular noun that ends in 's' is formed by adding an apostrophe followed by another 's'. In this case, since both "Rose" and "Alice" are singular nouns ending in 's', we need to add an apostrophe followed by 's' to show possession. Therefore, the correct sentences use "Rose's" and "Alice's" to indicate the relationship between the people mentioned.