Some of the arguments are valid by universal modus ponens or universal modus tollens; others are invalid and exhibit the converse or the inverse error. State which are valid, and which are invalid. Justify your answers.

11. All cheaters sit in the back row.

Monty sits in the back row.

Monty is a cheater

15. Any sum of two rational numbers is rational.

The sum r + s is rational.

The numbers r and s are both rational.