Which rule of inference is used in each of the following arguments? Check the correct answers.

1. If it is rainy, then the pool will be closed. It is rainy. Therfore, the pool is closed.

A. Disjunctive syllogism.
B. Addition.
C. Simplification.
D. Hypothetical syllogism.
E. Conjunction.
F. Modus tollens.
G. Modus ponens.

2. Colleen is a cat. Colleen is gray. Therefore Colleen is a gray cat.

A. Disjunctive syllogism.
B. Modus tollens.
C. Hypothetical syllogism.
D. Simplification.
E. Conjuction.
F. Addition.
G. Modus ponens.

3. Linda is an excellent swimmer. If Linda is an excellent swimmer, then she can work as a lifeguard. Therefore, Linda can work as a lifeguard.

A. Hypothetical syllogism.
B. Conjuction.
C. Modus tollens.
D. Addition.
E. Simplification.
F. Modus ponens.
G. Disjunctive syllogism.

4. If Pete had hit gold then Pete would be rich. Pete is not rich. Therefore, he did not hit gold.

A. Modus ponens.
B. Modus tollens.
C. Addition.
D. Conjuction.
E. Simplification.
F. Disjunctive syllogism.
G. Hypothetical syllogism.