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Propositional Logic·Intermediate·6 lessons·~320 min
How whole statements combine into logically assessable structures
What you'll learn
Lessons
Introduces propositional logic as the study of how whole statements combine, distinguishes atomic from compound statements, and establishes the discipline of seeing structure before symbolizing.
Examines each of the five standard connectives (negation, conjunction, disjunction, conditional, biconditional), how they translate natural-language forms, and the ambiguities students must resolve.
Teaches students to move from natural-language arguments to complete symbolic forms, assigning sentence letters consistently and preserving the inferential structure of the whole argument.
Introduces truth tables as a decision procedure for propositional validity, establishes the central logical equivalences, and teaches students to use truth tables to diagnose why an argument is valid or invalid.
Introduces the basic inference rules of propositional proof (modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, simplification, conjunction, and addition) and teaches students to build short formal proofs step by step.
An integrative lesson that asks students to run the full propositional cycle on mixed arguments: symbolize from English, classify validity, either prove the argument or build a truth-assignment counterexample, and explain the result in plain language.
How to study
Each lesson opens with a guided walkthrough — read it before the activity.
Look at why each step follows, not just what the answer is.
Know which rule applies and what would make the response weak before you start.
Optional context for the unit. Each lesson surfaces the concepts and rules it uses — these are here when you want the bigger picture.
A declarative sentence that is not further analyzed at the propositional level and is represented by a single sentence letter.
A statement formed from one or more simpler statements by the use of logical connectives.
An operator such as negation, conjunction, disjunction, conditional, or biconditional that forms a compound proposition from simpler ones.
The connective with the widest scope in a compound statement, which determines the statement's overall logical form.
The property that the truth value of a compound statement is completely determined by the truth values of its component parts.
A systematic listing of every possible assignment of truth values to the atomic parts of a compound statement together with the resulting value of the whole.
A statement that is true under every possible truth-value assignment to its atomic parts.
A statement that is false under every possible truth-value assignment to its atomic parts.
A relation between two statements that are true under exactly the same truth-value assignments.
The property of an argument whose conclusion cannot be false while all its premises are true.
A schematic pattern that licenses the derivation of a conclusion from one or more premises, such as modus ponens or disjunctive syllogism.