Translate the following arguments into symbolic form and use the first four rules of inference to derive the conclusion of each. The letters to be used for the simple statements are given in...

Translate the following arguments into symbolic form and use the first four rules of inference to derive the conclusion of each. The letters to be used for the simple statements are given in parentheses after each exercise. Use these letters in the order in which they are listed.

If a ninth planet exists, then its orbit is perpendicular to that of the other planets. Either a ninth planet is responsible for the death of the dinosaurs, or its orbit is not perpendicular to that of the other planets. A ninth planet is not responsible for the death of the dinosaurs. Therefore, a ninth planet does not exist. (E, O, R)