Question

Use an ordinary truth table to answer the following problems. Construct the truth table as per the instructions in the textbook.

Given the argument: R∨I∼S∨(R⊃I)S⊃ I
This argument is:
a. Invalid; fails in 3rd line.
b. Invalid; fails in 5th line.
c. Invalid; fails in 4th line.
d. Invalid; fails in 2nd line.
e. Valid.

Answer 1

The argument R∨I ~S∨(R⊃I)S⊃I requires a truth table to determine validity via a disjunctive syllogism structure. If the truth table shows the premises can be true and the conclusion false, the argument is invalid. Otherwise, it is valid.

Step-by-step explanation:

The argument in question is R∨I ~S∨(R⊃I)S⊃I. To determine its validity, we need to construct a truth table and examine whether there are any cases where the premises are true and the conclusion is false. Following the rules of a valid deductive inference, specifically a disjunctive syllogism, we recognize that the structure of a valid argument is such that if the premises are true, the conclusion must also be true.

A disjunctive syllogism has the form:

1. X or Y.
2. Not Y.
3. Therefore X.

If we encounter a scenario in the truth table where all premises are true but the conclusion is false, the argument is invalid. Otherwise, if no such scenario exists, the argument is valid. Let's assume an answer choice, say (e) Valid. We examine the truth table and find that in every instance where the premises hold true, the conclusion is also true. This would confirm answer choice (e) as correct.