Either Arithmetic and Logic Are Both Necessary or Logic and Geometry

question 217

Multiple Choice

Either arithmetic and logic are both necessary or logic and geometry are both necessary. If all knowledge is experiential, then even logic is not necessary. So, not all knowledge is experiential.
-Which of the following is the best translation into PL of this argument?

• A) (A • L) \( \lor \) (L • G) E ⊃ ∼L / ∼E
• B) N \( \lor \) ∼N E ⊃ L / ∼E
• C) (A \( \lor \) L) • (L \( \lor \) G) E ⊃ ∼L / ∼E
• D) N \( \lor \) ∼N E ⊃ ∼L / ∼E
• E) (A • L) \( \lor \) (L • G) E ⊃ L / ∼E

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Definitions:

Coefficient Of Correlation

An analytical measure that identifies the strength and directionality of a linear relationship involving two factors.

Coefficient Of Determination

The coefficient of determination, often denoted as R^2, is a statistic used in the context of statistical models whose main purpose is to provide a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.

Pearson Coefficient

A measure of the linear correlation between two variables X and Y, giving a value between -1 and 1.

Linear Relationship

A type of association where the change in a variable is consistent with the change in another variable, represented by a straight line on a graph.