Question

Consider the argument: "Each of five roommates, Melissa, Aaron, Ralph, Veneesha, and Keeshawn, has taken a course in discrete mathematics. Every student who has taken a course in discrete mathematics can take a course in algorithms. Therefore, all five roommates can take a course in algorithms next year."

Let r(x) denote "x is one of the five roommates listed".

Let d(x) denote "x has taken a course in discrete mathematics".

Let a(x) denote "x can take a course in algorithms".

(Hint: If you can turn the English argument into a Formal Logic proof, including the justification (reason) for each step, this will help you answer the following questions.)

Ch 01 Sec 6 Ex 14 (b) 3rd - Rules of inference

Identify the rule of inference that is used to arrive at the statement r(y) → a(y) from the statements r(y) → d(y) and d(y) → a(y).

(You must provide an answer before moving to the next part.)

Multiple Choice

• hypothetical syllogism

• simplification

• modus ponens

• modus tollens

Answer 1