Unit 1 · Logic and Proof

1.4Deductive Reasoning and Laws of Logic

Quick Answer

Law of Detachment: if p → q is true and p is true, then q is true. Law of Syllogism: if p → q and q → r are both true, then p → r is true. Deductive reasoning guarantees conclusions when premises are true.

Essential Question

How do the Law of Detachment and Law of Syllogism allow us to draw guaranteed conclusions from true premises?

Learning Goals

  • 1Distinguish deductive from inductive reasoning.
  • 2Apply the Law of Detachment.
  • 3Apply the Law of Syllogism.
  • 4Identify valid and invalid arguments.

Key Vocabulary

Deductive reasoning

Drawing specific conclusions from general principles using logic.

Law of Detachment

If p → q is true and p is true, then q must be true.

Law of Syllogism

If p → q and q → r are both true, then p → r is true.

Valid argument

An argument in which the conclusion follows necessarily from the premises.

Full lesson content coming soon

Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.