Answer:
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
