Boolean logic glossary: terms, meanings and examples
Sixty terms of Boolean algebra, propositional logic and rule testing, each defined in its first sentence, with a computed example and its Spanish equivalent.
The glossary covers the words the other pages rely on: the kinds of formula (tautology, contradiction, contingency), the building blocks of normal forms (literal, clause, minterm, maxterm, implicant), the vocabulary of arguments (premise, conclusion, validity, soundness, counterexample, vacuous truth), the hardware words (gate, universal gate, fan-out) and the testing words (decision table, condition and decision coverage, MC/DC, independence pair, mutant).
Where a term has a computable example, the page shows it: a tautology page proves A OR NOT A on every row, a minterm page shows the canonical sum, an MC/DC page shows the independence pairs the engine finds for a three-input rule. The Spanish term is given on every English page and the English term on every Spanish page, because many readers learn in one language and read documentation in the other.
Terms are written so that the first sentence can stand alone as the definition.
- Truth table: meaning and examples
A truth table lists every combination of values the inputs of a formula can take, one row per combination, and the value the formula gives on each. With n inputs it has 2 to the power n rows. - Tautology in logic: meaning and examples
A tautology is a formula that is true on every row of its truth table, whatever values its variables take. A OR NOT A is the simplest one. - Contradiction in logic: meaning and examples
A contradiction is a formula that is false on every row of its truth table: no assignment of values to its variables makes it true. A AND NOT A is the simplest one. - Contingency in logic: meaning and examples
A contingency is a formula that is true on some rows of its truth table and false on others: neither a tautology nor a contradiction. Almost every formula that does real work is one. - Satisfiable in logic: meaning and examples
A formula is satisfiable when at least one assignment of values to its variables makes it true. The assignment that does so is its witness, or satisfying assignment. - Valid argument in logic: meaning and examples
An argument is valid when its conclusion is true in every case where all its premises are true: no row of the truth table has every premise true and the conclusion false. - Sound argument in logic: meaning and examples
A sound argument is a valid argument whose premises are all actually true. Soundness adds a claim about the world to a claim about form, so a truth table can establish only half of it. - Counterexample in logic: meaning and examples
A counterexample is one assignment of values that refutes a claim: for an argument, a row where every premise is true and the conclusion is false; for a tautology claim, a row where the formula is… - Witness (satisfying assignment): meaning and examples
A witness, or satisfying assignment, is one assignment of values to the variables that makes a formula true. It is the evidence the engine shows whenever a verdict depends on a single row existing. - Premise in logic: meaning and examples
A premise is a statement an argument takes as given. The conclusion is what is claimed to follow from the premises taken together, and validity is tested only on the rows where every premise is true. - Conclusion in logic: meaning and examples
The conclusion is the single statement an argument claims to establish from its premises. An argument is valid when the conclusion is true on every row where all the premises are true. - Logical equivalence: meaning and examples
Two formulas are logically equivalent when they have the same truth value on every row of a truth table over their combined variables. - Literal in logic: meaning and examples
A literal is a variable or the negation of a variable: A and NOT B are literals, A AND B and NOT (A OR B) are not. Literals are the atoms from which clauses, terms and normal forms are built. - Clause in logic: meaning and examples
A clause is an OR of literals, such as A OR NOT B. A formula in conjunctive normal form is an AND of clauses, and a clause is satisfied by any assignment that makes at least one of its literals true. - Term (product term): meaning and examples
A term, or product term, is an AND of literals, such as A AND NOT B. A sum of products is an OR of terms, and a term is true only on the rows where every one of its literals is true. - Minterm: meaning and examples
A minterm is an AND of every variable of a function, each plain or negated, so it is true on exactly one row of the truth table. A function is the OR of the minterms of its true rows. - Maxterm: meaning and examples
A maxterm is an OR of every variable of a function, each plain or negated, so it is false on exactly one row of the truth table. A function is the AND of the maxterms of its false rows. - Sum of products (SOP): meaning and examples
A sum of products (SOP) is an OR of AND-terms of literals, such as (A AND B) OR (NOT A AND C). - Product of sums (POS): meaning and examples
A product of sums (POS) is an AND of OR-clauses of literals, such as (A OR B) AND (NOT A OR C). It is the same shape as conjunctive normal form, written with AND as a product and OR as a sum. - Disjunctive normal form (DNF): meaning and examples
Disjunctive normal form (DNF) is an OR of terms, each term an AND of literals. - Conjunctive normal form (CNF): meaning and examples
Conjunctive normal form (CNF) is an AND of clauses, each clause an OR of literals. It is the input format of SAT solvers, and every formula has an equivalent CNF. - Canonical form in Boolean algebra: meaning and examples
A canonical form is a normal form that is unique for each function over a fixed variable order: the sum of minterms Σm(…) or the product of maxterms ΠM(…). - Negation normal form: meaning and examples
A formula is in negation normal form (NNF) when NOT appears only directly on variables and the only other operators are AND and OR. It is the halfway point of every conversion to CNF or DNF. - Implicant: meaning and examples
An implicant of a function is a product term that implies it: wherever the term is true, the function is true. On a Karnaugh map, an implicant is any legal group of cells that all contain 1. - Prime implicant: meaning and examples
A prime implicant is an implicant that cannot be made any larger: removing any literal from it would make it cover a row where the function is false. - Essential prime implicant: meaning and examples
An essential prime implicant is a prime implicant that covers at least one true row no other prime implicant covers. - Don’t-care condition: meaning and examples
A don't-care condition is an input combination that never occurs, or whose output nobody needs, so the designer may treat its cell as 1 or 0, whichever gives a larger group. - Gray code: meaning and examples
Gray code is an ordering of binary numbers in which consecutive values differ in exactly one bit: 00, 01, 11, 10. - Karnaugh map (K-map): meaning and examples
A Karnaugh map (K-map) is a truth table redrawn as a grid in Gray-code order, so that cells differing in one variable are neighbours. - Quine–McCluskey method: meaning and examples
The Quine–McCluskey method is a tabular procedure for simplifying a Boolean function: list the minterms in binary, merge pairs that differ in one bit until no merge remains, and the survivors are the… - Logic gate: meaning and examples
A logic gate is a device, physical or drawn, that computes one Boolean operator: it takes one or more binary inputs and produces one binary output according to a fixed truth table. - Universal gate: meaning and examples
A universal gate is one from which every Boolean function can be built using no other kind of gate. NAND and NOR are the two universal gates; AND, OR and NOT are not universal on their own. - Fan-out in digital logic: meaning and examples
Fan-out is the number of gate inputs that one signal drives. In a logic diagram it is the branching of a wire; in a formula it is a variable or subexpression that appears more than once. - Combinational logic: meaning and examples
Combinational logic is a circuit whose outputs depend only on its current inputs, with no memory and no feedback. - Boolean function: meaning and examples
A Boolean function maps each combination of n binary inputs to one binary output. It is the mathematical object a truth table describes, and many different expressions can denote the same function. - Boolean expression: meaning and examples
A Boolean expression is a formula built from variables, the constants TRUE and FALSE, and operators such as AND, OR and NOT, with parentheses for grouping. - Proposition in logic: meaning and examples
A proposition is a statement that is either true or false: “the door is open”, “7 is prime”. - Logical connective: meaning and examples
A logical connective is an operator that joins propositions into a compound whose truth value is fixed by the truth values of its parts: AND, OR, NOT, the conditional ->, the biconditional <-> and… - Antecedent in logic: meaning and examples
The antecedent is the “if” part of a conditional: in A -> B, A is the antecedent and B the consequent. A conditional is false only when its antecedent is true and its consequent false. - Consequent in logic: meaning and examples
The consequent is the “then” part of a conditional: in A -> B, B is the consequent. The conditional promises the consequent only when the antecedent holds, and says nothing when it does not. - Converse in logic: meaning and examples
The converse of the conditional A -> B is B -> A: the same two parts with the arrow reversed. - Contrapositive in logic: meaning and examples
The contrapositive of A -> B is NOT B -> NOT A: both parts negated and the arrow reversed. A conditional and its contrapositive are logically equivalent, so either can stand in for the other. - Inverse of an implication: meaning and examples
The inverse of the conditional A -> B is NOT A -> NOT B: both parts negated, arrow unchanged. - Vacuous truth in logic: meaning and examples
A statement is vacuously true when it holds only because the case it speaks about never arises: a conditional with a false antecedent, a claim about every member of an empty set, an argument whose… - Assumption (domain constraint): meaning and examples
An assumption, or domain constraint, is a formula declared to hold in every admissible case of a model. - Decision table: meaning and examples
A decision table lists the conditions a rule depends on, the combinations of their values that matter, and the outcome for each combination. - Decision coverage in software testing: meaning and examples
Decision coverage is reached when every decision in the code, every Boolean expression that steers control, has evaluated to both TRUE and FALSE during the tests. It is also called branch coverage. - Condition coverage in software testing: meaning and examples
Condition coverage is reached when every atomic condition inside a decision has taken both the value TRUE and the value FALSE during the tests. - MC/DC (modified condition/decision coverage): meaning and examples
MC/DC, modified condition/decision coverage, requires that every condition in a decision be shown to independently affect the outcome: for each condition, a pair of tests that differ only in that… - Independence pair in MC/DC: meaning and examples
An independence pair for a condition is two test cases that differ only in the value of that condition and produce different decision outcomes. - Mutation testing: meaning and examples
Mutation testing judges a test suite by planting small deliberate faults, mutants, in the rule under test and checking whether the tests notice. - Mutant in mutation testing: meaning and examples
A mutant is a copy of a rule with one small deliberate change. It is killed when some test gives a different result on the mutant than on the original, and it survives when every test passes on both. - Regression test: meaning and examples
A regression test checks that behaviour which used to be right is still right after a change. - Test oracle (expected result): meaning and examples
A test oracle is whatever supplies the expected result of a test: the thing an actual result is compared against. - Exhaustive check: meaning and examples
An exhaustive check evaluates a property on every assignment of the variables, so its verdict is a proof rather than a sample. - SAT solver: meaning and examples
A SAT solver is a program that decides whether a Boolean formula is satisfiable, returning a satisfying assignment when one exists, by search rather than by enumerating every row. - Subcircuit (reusable block): meaning and examples
A subcircuit is a named, reusable block of logic with its own inputs and output, defined once and used inside other formulas.in progress - Variable and its glossary description: meaning and examples
A variable is an input of a model, a name that takes the value TRUE or FALSE on each row. - Decision mode vs argument mode: meaning and examples
Decision mode is the way of working in which a model has named outputs, each a formula over the inputs, and the checks ask about those outputs. - Notation (words, programming, mathematical, algebra): meaning and examples
Notation is the set of symbols used to write Boolean formulas: words (AND, OR, NOT), programming operators (&&, ||, !), mathematical logic (∧, ∨, ¬) or Boolean algebra (·, +, overbar).
Questions
Why both “mintérmino” and “minitérmino” on the Spanish pages?
Both spellings are in use; the second appears in Google's own suggestions for Spanish searches. The pages carry the standard form first and mention the variant so that either search lands here.
Generated from the Tangibool engine, semantics tangibool-semantics/1, engine 1.0.0, build . Every table, map, simplification and verdict on these pages was computed by the Tangibool engine when the site was built, and every claim was re-checked by the same exact checker the app uses. Limits are stated where they apply. © 2026 Foreranger LTD.