Deductive Reasoning and Logical Laws

Flashcards covering key vocabulary, definitions, and symbolic representations of deductive reasoning, the Law of Detachment, and the Law of Syllogism.

Deductive Reasoning

The process of reasoning logically and drawing a conclusion from given facts + statements.

Law of Detachment

A rule stating that given a conditional statement, if the hypothesis is true, then the conclusion is true.

Therefore Symbol ($\therefore$)

The mathematical symbol $\therefore$, which stands for 'therefore'.

Law of Syllogism

A rule that allows you to draw a conclusion from two conditional statements in which the conclusion of the first statement is the hypothesis of the second statement.

Symbolic Map for Law of Detachment

The logical representation where given $p \rightarrow q$ and $p$, the conclusion is $\therefore q$.

Symbolic Map for Law of Syllogism

The logical representation where given $p \rightarrow q$ and $q \rightarrow r$, the conclusion is $\therefore p \rightarrow r$.

Hypothesis

The component of a conditional statement which, if true under the Law of Detachment, guarantees that the conclusion is also true.

Conclusion

The resulting statement that is proven true in a conditional statement when the hypothesis is established as true.