Truth tables can (Points : 1)
display all the possible truth values involved with a set of sentences.
determine what scientific claims are true.
determine if inductive arguments are strong.
determine if inductive arguments are weak.
Truth tables can display all the possible truth values involved with a set of sentences.
To create a truth table, you need to list all the possible combinations of truth values for the atomic propositions (individual statements) in the given set of sentences. Each row of the truth table corresponds to one of the possible combinations. For example, if you have two atomic propositions, A and B, there are four possible combinations of truth values: true-true, true-false, false-true, and false-false.
Once you have listed all the combinations, you can evaluate the truth values of compound propositions (statements that are formed by combining atomic propositions using logical connectives such as "and", "or", and "not"). This allows you to see the truth value of the compound proposition for each combination of truth values.
By examining the truth values in the truth table, you can determine various properties of the logical relationships between the atomic and compound propositions. For example, you can determine if a compound proposition is tautology (always true), contradiction (always false), or contingent (true in some cases and false in others).
Truth tables are commonly used in logic and mathematical proofs to analyze the logical consequences of a set of sentences and to determine the truth values of compound propositions based on the truth values of their atomic components. They can help display and understand the logical relationships and possibilities within a given set of sentences. However, truth tables themselves do not directly determine the truth of scientific claims or the strength of inductive arguments.