Question 4 What rules of inference where used for each of the following arguments? (a) Kangaroos live in Australia and are marsupials. Therefore, kangaroos are marsupials. (b) Linda is an excellent...

Discret Math

Extracted text: Question 4 What rules of inference where used for each of the following arguments? (a) Kangaroos live in Australia and are marsupials. Therefore, kangaroos are marsupials. (b) 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. Please type your answer in the space provided.


Extracted text: Question 8 Steps below show that the premises "Linda, a student in this class, owns a red convertible" and "Everyone who owns a red convertible has gotten at least one speeding ticket" imply conclusion "Someone in this class has gotten a speeding ticket." Fill in the blanks. Let R(x) = "x owns a red convertible", S(x) = "x has gotten at least one speeding ticket", and C(x) = "x is a student in our class" , where the domain of x consists of all people in the world. Premises in logical form, therefore, will be C(linda), C(Linda) a R(Linda) and Vx(R(x)→ S(x)). (1) Vx(R(x)→ S(x)) [a] (2) R(Linda) → S(Linda) [b] instantiation from (1) (3) C(Linda) A R(Linda) Premise (4) C(Linda) [c] from (3) (5) R(Linda) [d] from (3) (6) S(Linda) Modus ponens from [e] and (5) (7) C(Linda) A S(Linda) [f] from (4) and (6) (8) 3x(C(x) A S(x)) Existential [g] from [h] Step (8) expressed in words is "Therefore, someone in the class has gotten at least one speeding ticket".