Boolean algebra
True-false mathematics
Boolean algebra is the branch of mathematics dealing with logical operations on true/false values.
Variables take only two states—true or false, 1 or 0—and combine through operations like AND, OR, and NOT.
It underlies digital circuit design and computer programming, where conditions must evaluate to binary outcomes.
Named for mathematician George Boole.
Mathematics of abstract collections
- latticeOpenwork of crossed strips
- De Morgan's lawsLogical negation distribution rules
- binaryConsisting of two parts
- zeroNumerical absence of quantity
one · universe · empty set · complement · intersection · union · symbolic logic
Statement expressing a judgment
- conjunctionWord joining clauses together
- disjunctionState of being apart
- negationDenial or cancellation
- implicationIndirect suggestion or consequence
equivalence · tautology · contradiction · predicate · antecedent · consequent · axiom · theorem
Hinged barrier in fence
- AND gateCircuit outputting true when both inputs true
- NANDNegated-and logic operation
- XORTrue iff inputs differ
- flip-flopSudden change of position
multiplexer · demultiplexer · encoder · decoder · combinational · sequential · Karnaugh map · minimization
set theory
Mathematics of abstract collections
- latticeOpenwork of crossed strips
- De Morgan's lawsLogical negation distribution rules
- binaryConsisting of two parts
zero · one · universe · empty set · complement · intersection · union · symbolic logic
proposition
Statement expressing a judgment
- conjunctionWord joining clauses together
- disjunctionState of being apart
- negationDenial or cancellation
implication · equivalence · tautology · contradiction · predicate · antecedent · consequent · axiom · theorem · proof
gate
Hinged barrier in fence
- AND gateCircuit outputting true when both inputs true
- NANDNegated-and logic operation
- XORTrue iff inputs differ
flip-flop · multiplexer · demultiplexer · encoder · decoder · combinational · sequential · Karnaugh map · minimization · truth table
conditional
Dependent on prerequisites
false · filter · mask · comparison · assertion
- algebras
- logicpremise, premises, conclusion, conclusions, inference
- applied mathlinear programming, differential equations, statistical methods, probability, statistics
- abstract algebragroup, isomorphism, commutator, congruence, ideal
- Boolean logicand, or, not, true, false
- digital circuitslogic gate, AND gate, flip-flop, latch, logic gates
Boolean algebraarithmetic
Mathematics of basic operations
calculus · differential equations · integral calculus · elementary algebra · linear algebra