Biconditional
A biconditional is true when two propositions have the same truth value.
Definition · Example · CSE Use →Logic & Boolean Algebra
Definitions, examples and Computer Science applications for this mathematics subject.
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Boolean Algebra
Boolean algebra is an algebraic system for variables that take truth values such as 0/1 or false/true.
Definition · Example · CSE Use →Conjunction
A conjunction p AND q is true only when both propositions are true.
Definition · Example · CSE Use →Conjunctive Normal Form
Conjunctive normal form represents a Boolean formula as an AND of one or more OR clauses.
Definition · Example · CSE Use →Contradiction
A contradiction is a logical expression that is false for every possible truth assignment.
Definition · Example · CSE Use →De Morgan’s Laws
De Morgan’s laws describe how negation distributes over AND and OR operations.
Definition · Example · CSE Use →Disjunction
A disjunction p OR q is true when at least one proposition is true.
Definition · Example · CSE Use →Disjunctive Normal Form
Disjunctive normal form represents a Boolean formula as an OR of one or more AND terms.
Definition · Example · CSE Use →Exclusive OR
Exclusive OR is true when exactly one of two inputs is true.
Definition · Example · CSE Use →Existential Quantifier
The existential quantifier states that a predicate is true for at least one element in a domain.
Definition · Example · CSE Use →Implication
An implication p → q is false only when p is true and q is false.
Definition · Example · CSE Use →Logical Equivalence
Two logical expressions are logically equivalent when they have identical truth values for all inputs.
Definition · Example · CSE Use →NAND
NAND is the negation of AND and is false only when all inputs are true.
Definition · Example · CSE Use →Negation
Negation reverses the truth value of a proposition.
Definition · Example · CSE Use →NOR
NOR is the negation of OR and is true only when all inputs are false.
Definition · Example · CSE Use →Predicate
A predicate is a statement containing variables that becomes a proposition when values are assigned or quantified.
Definition · Example · CSE Use →Proposition
A proposition is a declarative statement that is either true or false.
Definition · Example · CSE Use →Tautology
A tautology is a logical expression that is true for every possible truth assignment.
Definition · Example · CSE Use →Truth Table
A truth table lists the truth value of a logical expression for every possible combination of inputs.
Definition · Example · CSE Use →Universal Quantifier
The universal quantifier states that a predicate is true for every element in a domain.
Definition · Example · CSE Use →