Mathbase module
Logic & Quantifiers
Work through these bite-sized lessons. Each subsection has reading, notebook prompts, and an optional AI critique to refine your understanding.
Recommended: move in order, but you can jump around if you’re reviewing specific ideas.
Subsections
Click into a subsection to read, practice, and get feedback on your explanation.
Propositions, Statements, and Connectives
A proposition is a statement with a definite truth value. Logical connectives allow us to combine them into more complex statements.
Truth Tables & Logical Equivalence
Truth tables measure truth under all conditions. Logical equivalence means two statements behave identically in every case.
Implications & The If and Only If
Implications are only false when the hypothesis is true and the conclusion is false. IFF means two statements imply each other.
Quantifiers (∀, ∃) and How They Work
Quantifiers formalize “for all” and “there exists.” Their order changes the meaning of statements dramatically.
Negation of Complex Statements
Negations flip quantifiers and break apart logical structure using equivalence rules like De Morgan’s laws.
Mistakes Students Make With Quantifiers
Most errors come from misunderstanding scope or quantifier order. Always ask: “What depends on what?”