Is it possible to have different access modifiers on the get/set methods of a property? Justify

Yes - but all access modifiers are set when you declare the item and cannot be changed after that.

Different modifiers are particularly useful with properties, as they allow the outside world to have limited access to your variables.

For example, you might have a string property:

public string Text { get; private set; }

Where the outside world can read the text you are processing at any time, but only the class that created the property can ever modify it.