Statements, Symbolic Representation, and Tautologies
Formal logic can represent the statements we use in English to communicate facts or information. A statement (or proposition) is a sentence that is either true or false.
In English, simple statements are combined with connecting words like and to make more interesting compound statements.
Identify the antecedent and consequent in an implication statement
This quiz tests your understanding of practical applications of formal logic. It covers how search engines utilize logical connectives (AND, OR, NOT) to refine web queries, how logical expressions simplify program code and control execution flow, and how electronic gates implement these truth tables directly in computer circuitry.
The foundational concepts of algorithms in logic, including truth table scaling, pseudocode structure, shortcut tautology testing for conditional expressions, and identifying contradictions in truth assignments
Introduces what counts as a genuine logical statement, then practices evaluating the truth values of simple conjunctions, disjunctions, and conditionals built from basic number facts.
Practices evaluating compound well-formed formulas (WFFs) built from AND, OR, and negation, given specific truth-value assignments for each variable.
Covers translating everyday phrases such as "sufficient condition," "necessary condition," and "only if" into symbolic conditional statements, along with writing and negating simple disjunctions and conjunctions.
Covers translating more complex compound statements back and forth between English sentences and symbolic logical notation.
Covers testing logical equivalence, identifying the contrapositive of a conditional, verifying tautologies, and applying propositional logic to search-engine queries, program conditions, and combinatorial counting.
Covers which sets of logical connectives are functionally complete, extending truth tables to three-valued logic, and solving classic self-referential logic puzzles.