Question

What rule of inference is used in each of these argu- ments? a) Kangaroos live in Australia and are marsupials. Therefore, kangaroos are marsupials. b) It is either hotter than 100 degrees today or the pollu- tion is dangerous. It is less than 100 degrees outside today. Therefore, the pollution is dangerous. c) Linda is an excellent swimmer. If Linda is an ex- cellent swimmer, then she can work as a lifeguard. Therefore, Linda can work as a lifeguard. d) Stevewillworkatacomputercompanythissummer. Therefore, this summer Steve will work at a computer company or he will be a beach bum. e) If I work all night on this homework, then I can an- swer all the exercises. If I answer all the exercises, I will understand the material. Therefore, if I work all night on this homework, then I will understand the material.

Answer 1

A. Simplification

B. Disjunctive Syllogism

C. Modus Ponens

D. Addition

E. Hypothetical Syllogism

Step-by-step explanation:

(a) Given that k = the proposition “Kangaroos live in Australia.”

m = the proposition “Kangaroos are marsupials.”

Hence, k ∧ m→ k = Simplification

(b) Given that k = the proposition ”Hotter than 100 degrees today.”

m = the proposition ”Pollution is dangerous.”

Hence (k ∨ m) ∧ ¬k → m = Disjunctive syllogism

(c) Given that k be the proposition ”Linda is an excellent swimmer.”

m = the proposition ”Can work as a lifeguard.”

Hence, k ∧ (k → m) → m = Modus ponens

(d) Given that k =the proposition ”Steve will work at a computer company this summer.”

m = the proposition ”Steve will be a beach bum.”

Hence, k → k ∨ m. = Addition

e) Given that k = the proposition " I work all night on this homework."

m = the proposition "I will answer all the exercises"

n = the proposition "I will understand the material."

(k → m) ∧ (m → n) → (k → n) = Hypothetical Syllogism