How to compare sums of infimum (or supremum) of two sets?

Question

1. $ \sup\{x_n+y_n\}⩽\sup\{x_n\}+\sup\{y_n\} $
2. $ \sup\{x_n+y_n\}⩾\sup\{x_n\}+\sup\{y_n\} $
3. $ \sup\{x_n−y_n\}⩽\sup\{x_n\}−\sup\{y_n\} $
4. $ \sup\{x_n−y_n\}⩾\sup\{x_n\}−\sup\{y_n\} $
5. $ \sup\{x_n+y_n\}⩽\sup\{x_n\}+\inf\{y_n\} $
6. $ \sup\{x_n+y_n\}⩾\sup\{x_n\}+\inf\{y_n\}$

Which of this expression are correct ? Why or why not ? How can check it by myself?