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) . 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.

A.   Simplification

B.   Disjunctive Syllogism

C.  Modus Ponens

D.  Addition

E.  Hypothetical Syllogism

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

carefully examine the map above. based on your knowledge of colonialism in africa, the area attributed to belgium on this map is most likely the democratic republic of the congo.

answer; repetitive thoughts; ritualistic behaviors;