Question

What rule of inference is used in each of these arguments?
a) Alice is a mathematics major. Therefore, Alice is either a mathematics major or a computer science major.
b) Jerry is a mathematics major and a computer science major. Therefore, Jerry is a mathematics major.
c) If it is rainy, then the pool will be closed. It is rainy. Therefore, the pool is closed.
d) If it snows today, the university will close. The university is not closed today. Therefore, it did not snow today.
e) If I go swimming, then I will stay in the sun too long. If I stay in the sun too long, then I will sunburn. Therefore, if I go swimming, then I will sunburn.

Short answer

The rule of interference using in argument can be found.

Step-by-step solution

Find argument form of a

Let’s take p is the proposition and “Alice is a mathematics major” and q be the proposition “Alice is a computer science major”. The argument is in the form of abstract. \(p \vee q.\)The argument is in Disjunctive addition form.

Find argument form of b

Let’s take p is the proposition and “Jerry is a mathematics major” and q be the proposition “Jerry is a computer science major”. The argument is in the form of abstract. \(p \wedge q.\)The argument is in Conjunctive simplification form.

Find argument form of c

Let’s take p is the proposition and “It is rainy” and q be the proposition “the pool will be closed”. The argument is in the form of abstract p;q. The argument is in Modus Ponens form.

Find argument form of d

Let’s take p is the proposition and “It snows today” and q be the proposition “the university will close”. The argument is in the form of abstract ~q and ~p. The argument is in Modus Tollens form.

Find argument form of e

Let’s take p is the proposition and “I go swimming” and q be the proposition “I will stay in the sun too long” and r be the “I will sunburn”. The argument is in the form of abstract. If p then q; If q then r; If p then r. The argument is in Hypothetical syllogism form.