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

Given the argument:
P ∨ J / ∼(J • ∼ P) // J ≡ ∼ P
This argument is:
a. Valid.
b. Invalid; fails in 4th line.
c. Invalid; fails in 3rd line.
d. Invalid; fails in 1st line.
e. Invalid; fails in 2nd line.

1 Answer

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Final answer:

To determine the validity of the logical argument, a truth table must be constructed to analyze if there is any scenario where the premises are true and the conclusion false, indicating invalidity.

Step-by-step explanation:

Validity of a Logical Argument Using a Truth Table

To assess the validity of the argument P ∨ J / ¬(J • ¬ P) // J ≡ ¬ P, we need to create a truth table. The argument is valid if, when the premises are true, the conclusion is also true. This means that whenever P ∨ J (P or J) is true, and ¬(J • ¬ P) (not both J and not P) is also true, the conclusion J ≡ ¬ P (J is equivalent to not P) must be true as well. If there is any case in which the premises are true and the conclusion is false, then the argument is invalid.

A disjunctive syllogism is an argument form involving an "or" statement (disjunct) and the negation of one of its parts. It leads to the conclusion that the other part must be true. In this case, we are dealing with an argument that has a similar logical form. The truth table we construct would help us understand whether the logical form holds in this case by evaluating all possible combinations of truth values for P and J.

After constructing the truth table, we would look for a row where the premises are true, and the conclusion is false. If such a row exists, the argument fails, and the line number of that row would correspond to the answer choice indicating the argument's invalidity. If there is no such row, the argument is valid.

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