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Mathematical table used in logic
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which
Truth_table
Concept in theoretical computer science
In computability theory, a truth-table reduction is a type of reduction from a decision problem A {\displaystyle A} to a decision problem B {\displaystyle
Truth-table_reduction
Branch of logic
the truth functions of conjunction, disjunction, implication, biconditional, and negation. Some sources include other connectives, as in the table below
Propositional_logic
Function in logic
exactly one truth value which is either true or false, and every logical connective is truth functional (with a correspondent truth table), thus every
Truth_function
Graphical set representation involving overlapping shapes
expand a method proposed by Edward W. Veitch; this work would rely on the truth table method precisely defined by Emil Post and the application of propositional
Euler_diagram
operators and symbols in Unicode Non-logical symbol Polish notation Truth function Truth table Wikipedia:WikiProject Logic/Standards for notation "Named character
List_of_logic_symbols
Logical connective
argument is false. This semantics can be shown graphically in the following truth table: One can also consider the equivalence A → B ≡ ¬ ( A ∧ ¬ B ) ≡ ¬ A ∨
Material_conditional
Logic constructed only from NAND gates
NOR logic. A NAND gate is an inverted AND gate. It has the following truth table: In CMOS logic, if both of the A and B inputs are high, then both the
NAND_logic
Logical connective AND
empty set of operands) is often defined as having the result true. The truth table of A ∧ B {\displaystyle A\land B} : In systems where logical conjunction
Logical_conjunction
Electronic circuit with two stable states
phases prevent data transparency as in a master–slave flip-flop. The truth table below shows that when the enable input is 0, the D input has no effect
Flip-flop_(electronics)
Method for solving one problem using another
most to the least restrictive, are polynomial-time many-one reductions, truth-table reductions, and Turing reductions. The most frequently used of these
Polynomial-time_reduction
Making other gates using just NOR gates
approach). A NOR gate is logically an inverted OR gate. It has the following truth table: A NOR gate is a universal gate, meaning that any other gate can be represented
NOR_logic
Computer operation which manipulates invidual bits of data
There are 16 possible truth functions of two binary variables; this defines a truth table, termed a LUT2 lookup table, a.k.a. a Boolean function
Bitwise_operation
Symbol connecting formulas in logic
Modal operator Propositional calculus Term logic Tetralemma Truth function Truth table Truth values Chao, C. (2023). 数理逻辑：形式化方法的应用 [Mathematical Logic:
Logical_connective
Logical operation
true, if — and only if — at least one of the propositions is false. The truth table of A ↑ B {\displaystyle A\uparrow B} is as follows. The Sheffer stroke
Sheffer_stroke
Function returning one of only two values
with k {\displaystyle k} arguments; equal to the number of different truth tables with 2 k {\displaystyle 2^{k}} entries. Every k {\displaystyle k} -ary
Boolean_function
Standard form of a boolean function
(y\land z))\\\end{array}}} The full DNF of a formula can be read off its truth table. For example, consider the formula ϕ = ( ( ¬ ( p ∧ q ) ) ↔ ( ¬ r ↑ (
Disjunctive_normal_form
Device performing a Boolean function
constructed). Ludwig Wittgenstein introduced a version of the 16-row truth table as proposition 5.101 of Tractatus Logico-Philosophicus (1921). Walther
Logic_gate
Table in automata theory and sequential logic
on the current state and other inputs. It is essentially a truth table or a control table, in which the inputs include the current state along with other
State-transition_table
Logic formula
variables produces 16 truth-table rows and 16 squares and therefore 16 minterms. Each Karnaugh-map square and its corresponding truth-table evaluation represents
Propositional_formula
Binary operation that is true if and only if both operands are false
connectives. This can be proved by first showing, with a truth table, that ¬ A {\displaystyle \neg A} is truth-functionally equivalent to A ↓ A {\displaystyle
Logical_NOR
Rule of logical inference
through a truth table. In instances of modus tollens we assume as premises that p → q is true and q is false. There is only one line of the truth table—the
Modus_tollens
If and only if relation
both operands are false or both operands are true. The following is a truth table for A ↔ B {\displaystyle A\leftrightarrow B} : When more than two statements
Logical_biconditional
Digital logic circuit
y_{n}=x_{1}x_{2}+(x_{1}+x_{2})y_{n-1}} , which corresponds to the following truth table: This table can be turned into a circuit using the Karnaugh map. However, the
C-element
In logic, a statement which is always true
method of truth tables illustrated above is provably correct – the truth table for a tautology will end in a column with only T, while the truth table for a
Tautology_(logic)
Logic gate
XOR gate with inputs A and B. The behavior of XOR is summarized in the truth table shown on the right. There are three schematic symbols for XOR gates:
XOR_gate
Graphical method to simplify Boolean expressions
race conditions. The required Boolean results are transferred from a truth table onto a two-dimensional grid where, in Karnaugh maps, the cells are ordered
Karnaugh_map
Statement that is true regardless of the truth or falsity of its constituent propositions
Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity
Logical_truth
True when either but not both inputs are true
{\displaystyle \nleftrightarrow } , ≢ {\displaystyle \not \equiv } , and ^. The truth table of A ↮ B {\displaystyle A\nleftrightarrow B} shows that it outputs true
Exclusive_or
Digital logic gate
two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an "equivalence
XNOR_gate
Operations transforming individual bits of integral data types
the operands rather than the truth value of the operands. Bitwise binary AND performs logical conjunction (shown in the table above) of the bits in each
Bitwise_operations_in_C
Logic gate type
and truth table: Q = ( A ∧ B ∧ C ) ∨ ( D ∧ E ∧ F ) ¯ . {\displaystyle Q={\overline {(A\wedge B\wedge C)\vee (D\wedge E\wedge F)}}.} Its logic table would
AND-OR-invert
Type of connective in logic
r ) {\displaystyle (q\land p)\lor (\neg q\land r)} and has the same truth table as the ternary conditional operator ?: in many programming languages
Conditioned_disjunction
Digital logic gate type
conjunction (∧) from mathematical logic – AND gates behave according to their truth table. A HIGH output (1) results only if all the inputs to the AND gate are
AND_gate
Logical connective OR
\models \psi } or both This semantics corresponds to the following truth table: In classical logic systems where logical disjunction is not a primitive
Logical_disjunction
Concept in mathematical logic
or Boolean operators is one that can be used to express all possible truth tables by combining members of the set into a Boolean expression. A well-known
Functional_completeness
Logical connective
interpretation under which all variables are assigned a truth value of "false" produces a truth value of "false" as a result of material nonimplication
Material_nonimplication
Concept in propositional logic
truth table that assigns "T" to all propositions ( P 1 {\displaystyle P_{1}} , P 2 {\displaystyle P_{2}} , ..., P n {\displaystyle P_{n}} ) the truth
Tautological_consequence
Algebraic manipulation of "true" and "false"
their truth table. There are eight such because the "odd-bit-out" can be either 0 or 1 and can go in any of four positions in the truth table. There
Boolean_algebra
In electronics, table of activating inputs
state) when the current state is known. They are similar to truth tables and state tables, but rearrange the data so that the current state and next state
Excitation_table
Terms to describe a conditional relationship between two statements
the consequent N must be true—if S is to be true (see third column of "truth table" immediately below). In other words, the antecedent S cannot be true
Necessity_and_sufficiency
3-volume treatise on mathematics, 1910–1913
use). But the symbols have no "interpretation" (e.g., no "truth table" or "truth values" or "truth functions") and modus ponens proceeds mechanistically,
Principia_Mathematica
Logical principle
{\displaystyle A\lor (B\land C)\iff (A\lor B)\land (A\lor C)} , the truth table is: As seen from the table, the columns for A ∨ ( B ∧ C ) {\displaystyle A\lor (B\land
Principle_of_distributivity
Concept in computability theory
result). A truth-table reduction or a weak truth-table reduction must present all of its oracle queries at the same time. In a truth table reduction,
Turing_reduction
Logical connective
\neg (P\leftarrow Q)} and ¬ P ∧ Q {\displaystyle \neg P\wedge Q} . The truth table of A ↚ B {\displaystyle A\nleftarrow B} . Converse nonimplication is
Converse_nonimplication
Type of quantum computer built out of Rydberg atoms
and thus does not pick up any phase, however the first one does. The truth table of this gate is given below. This is equivalent to a controlled-z gate
Neutral_atom_quantum_computer
Digital logic gate
logic gate that implements logical NOR - it behaves according to the truth table to the right. A HIGH output (1) results if both the inputs to the gate
NOR_gate
has to be true. This can be proven for any valid argument form using a truth table which shows that there is no situation in which there are all true premises
List_of_valid_argument_forms
Boolean polynomials as sums of monomials
These possible values are given in the following truth table: The information in the above truth table can be encoded in the following logical matrix:
Algebraic_normal_form
Universal reversible logic gate, applied in quantum computing
quantum-computing version where the bits are replaced by qubits. The truth table and permutation matrix are as follows (the permutation can be written
Toffoli_gate
Technical treatment of Boolean algebras
consider the i-th n-ary symbol to be nfi as done below in the section on truth tables. An equational theory in a given language consists of equations between
Boolean algebras canonically defined
Boolean_algebras_canonically_defined
Diagram that shows all possible logical relations between a collection of sets
sense that each region of Venn diagram corresponds to one row of the truth table. This type is also known as Johnston diagram. Another way of representing
Venn_diagram
System including an indeterminate value
truth tables showing the logic operations for Stephen Cole Kleene's strong logic of indeterminacy and Graham Priest's logic of paradox. If the truth values
Three-valued_logic
Method of comparing problems by transforming one into another in computability theory
{\displaystyle A(x)=B(f(x))} for all x {\displaystyle x} . Truth-table reducible: A {\displaystyle A} is truth-table reducible to B {\displaystyle B} if A {\displaystyle
Reduction (computability theory)
Reduction_(computability_theory)
Possessing negative truth value
related to Falsehood. Contradiction Logical truth Tautology (logic) (for symbolism of logical truth) Truth table Jennifer Fisher, On the Philosophy of Logic
False_(logic)
Study of computable functions and Turing degrees
such that each n is in A if and only if f(n) is in B. Truth-table reducibility: A is truth-table reducible to B if A is Turing reducible to B via an oracle
Computability_theory
avoided. In 1921, Emil Post would develop a theory of "truth functions" and their truth tables, which replace the notion of apparent versus real variables
History_of_type_theory
Digital electronic circuit
illustrated gate level example implements the simple encoder defined by the truth table, but it must be understood that for all the non-explicitly defined input
Encoder_(digital)
{\displaystyle (P\rightarrow Q)} in some logical system; and expressed as a truth-functional tautology or theorem of propositional logic. The principle was
Absorption_(logic)
Study of correct reasoning
define logic as the study of logical truths. Truth tables can be used to show how logical connectives work or how the truth values of complex propositions depend
Logic
Logical operation
{\displaystyle \neg P} is true, then P {\displaystyle P} would be false. The truth table of ¬ P {\displaystyle \neg P} is as follows: Negation can be defined
Negation
Cipher machines used by the German Army during World War II
(XOR) function, symbolised by ⊕. This is represented by the following "truth table", where 1 represents "true" and 0 represents "false". Other names for
Lorenz_cipher
Type of diagrammatic notation for logic
truth table. All the basic logical operations, or connectives, can be expressed using an R-diagrams as a more easily readable alternative to a truth table
Randolph_diagram
Logical operator in propositional calculus
if and only if both operands are false or both operands are true. The truth table of p EQ q (also written as p = q, p ↔ q, Epq, p ≡ q, or p == q) is as
Logical_equality
Conformity to reality
Truth is conformity to reality or fact. It contrasts with falsity or misrepresentation that fails to align with the world. Truth is typically treated as
Truth
Arrangement of information or data, typically in rows and columns
(Multiplication table) Logic (Truth table) In natural sciences, uses of tables include the periodic table in chemistry, and tide tables in oceanography
Table_(format)
Type of digital logic implemented by Boolean circuits
methods: a sum of products, or a product of sums. Consider the following truth table, which represents a 3-input combinatorial logic element taking inputs
Combinational_logic
Table specifying actions based on conditions
logic Semantic decision table Decision Model and Notation Truth table LI Jing (1 April 2015). "SEEM 3430 Tutorial: Decision Tables" (PDF). p. 23. Archived
Decision_table
false. Secondly, to be able to apply truth tables to describe a connective depends upon distributivity: a truth table is a disjunction of conjunctive possibilities
Is_Logic_Empirical?
Logic gate implementing negation
only one input, it is a unary operation and has the simplest type of truth table. It is also called the complement gate because it produces the ones'
Inverter_(logic_gate)
Topics referred to by the same term
Transaction translator, a particular unit in USB hubs tt-reduction (truth-table reduction), a kind of transformation used in computability theory <tt>
TT
Array that replaces runtime computation with a simpler array indexing operation
An n-bit LUT can encode any n-input Boolean function by storing the truth table of the function in the LUT. This is an efficient way of encoding Boolean
Lookup_table
that uses energy to perform formal logic operations through the use of truth tables. Early logical machines were mechanical devices that performed basic
Logical_machine
Concept in mathematical logic
triangle," because the definition of "triangle" is "three-sided polygon". A truth table makes it clear that S and the converse of S are not logically equivalent
Converse_(logic)
Value indicating the relation of a proposition to truth
Corresponding semantics of logical connectives are truth functions, whose values are expressed in the form of truth tables. Logical biconditional becomes the equality
Truth_value
Electronic circuits that utilize digital signals
an AND gate. Ludwig Wittgenstein introduced a version of the 16-row truth table as proposition 5.101 of Tractatus Logico-Philosophicus (1921). Walther
Digital_electronics
Topics referred to by the same term
HK, a telecommunication operator in Hong Kong wtt reduction, the weak truth-table reduction Wattle Glen railway station's station code Witton railway station's
WTT
Standard form of Boolean function
have. All truth-functional combinations can be expressed with 2 n {\displaystyle 2^{n}} disjunctions, one for each row of the truth table. In the example
Conjunctive_normal_form
Marker used in SQL databases to indicate a value does not exist
governing SQL three-valued logic are shown in the tables below (p and q represent logical states)" The truth tables SQL uses for AND, OR, and NOT correspond to
Null_(SQL)
If we construct a truth table for C we will find that it comes out T (true) on every row (and of course if we construct a truth table for the negation
Corresponding_conditional
Type of logical system
{\displaystyle \varphi \rightarrow \psi } , etc. is evaluated according to the truth table for the connective in question, as in propositional logic. Existential
First-order_logic
Cryptographic protocol for two-party computation
circuit and replaces 0 and 1 in the truth tables with the corresponding labels. The table below shows the truth table for an AND gate with two inputs w
Garbled_circuit
Computer program for complexity reduction of digital logic circuits
method developed by Willard Quine and Edward McCluskey. Starting with the truth table for a set of logic functions, by combining the minterms for which the
Espresso heuristic logic minimizer
Espresso_heuristic_logic_minimizer
Device that selects between several analog or digital input signals
{S_{0}}})+(B\cdot S_{0})} Which can be expressed as a truth table: Or, in simpler notation: These tables show that when S 0 = 0 {\displaystyle S_{0}=0} then
Multiplexer
Variety of storylike logic puzzle of apparent antinomy
leads to freedom. All can be determined by using Boolean algebra and a truth table. In Labyrinth, the protagonist's solution is to ask one of the guards:
Knights_and_Knaves
List of values of a mathematical function
Physics Standard normal table Table (information) Truth table Jurij Vega "Trigonometry Table: Learning of trigonometry table is simplified". Yogiraj notes
Mathematical_table
Assignment of meaning to the symbols of a formal language
logical connectives. The following table shows how this kind of thing looks. The first two columns show the truth-values of the sentence letters as determined
Interpretation_(logic)
Control logic tool developed by MathWorks
within a state chart. Stateflow also provides state transition tables and truth tables. Stateflow is generally used to specify the discrete controller
Stateflow
Digital circuit that produces sums from inputs
carry outputs, two half adders can be combined to make a full adder. The truth table for the half adder is: Various half adder digital logic circuits: Half
Adder_(electronics)
1921 philosophical work by Ludwig Wittgenstein
Wittgenstein is to be credited with the popularization of truth tables (4.31) and truth conditions (4.431) which now constitute the standard semantic
Tractatus Logico-Philosophicus
Tractatus_Logico-Philosophicus
Standard forms of Boolean functions
numbered 1102 = 610 and denoted m 6 {\displaystyle m_{6}} . Given the truth table of a logical function, it is possible to write the function as a "sum
Canonical_normal_form
Subfield of control engineering
aircraft elevator reactive controller through the use of a truth table and a state chart. The truth table defines how the controller reacts to detected faults
Fault_detection_and_isolation
Algorithm using holographic reduction
by its weighted truth table as a row vector and the constraint f v {\displaystyle f_{v}} be represented by its weighted truth table as a column vector
Holographic_algorithm
Universal reversible logic gate, applied in quantum computing
= C OR I1. If I1 = 0 and I2 = 1, then O2 = NOT C. We can encode the truth table in a hardware description language such as Verilog: module fredkin_gate
Fredkin_gate
Topological model
two entities, like a Truth table, the Three-way comparison, a Karnaugh map or a Venn diagram. Each output value is like a truth table line, that represent
DE-9IM
American semiotician (1925–2022)
displays its individual underlying logic truth table. In other words, after the simple and exact truth table code in the deep structure of XLA has been
Shea_Zellweger
Rule of replacement in propositional logic
a truth table: An example: we are given the conditional fact that if it is a bear, then it can swim. Then, all 4 possibilities in the truth table are
Material implication (rule of inference)
Material_implication_(rule_of_inference)
Computational theory
defined to be the truth table of the Boolean dictatorship function on the j {\displaystyle j} th coordinate, i.e., the truth table of f : { 0 , 1 } n
Long_code_(mathematics)
Hardware description language and software
in Redmond, Washington. ABEL includes both concurrent equation and truth table logic formats as well as a sequential state machine description format
Advanced Boolean Expression Language
Advanced_Boolean_Expression_Language
Number expressed in the base-2 numeral system
substantial reduction of effort. The binary addition table is similar to, but not the same as, the truth table of the logical disjunction operation ∨ {\displaystyle
Binary_number
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TRUTH TABLE
TRUTH TABLE
Girl/Female
American, Assamese, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Hawaiian, Hebrew, Hindu, Indian, Irish, Italian, Kannada, Malayalam, Marathi, Polish, Portuguese, Swedish, Swiss, Tamil, Telugu
Companion; Friend; Compassionate Friend; Season
Boy/Male
Tamil
Sathya Raj | ஸதà¯à®¯ ராஜ
Truth
Sathya Raj | ஸதà¯à®¯ ராஜ
Girl/Female
Spanish Swedish American Hebrew Greek Arthurian Legend English German Teutonic
Truth.
Biblical
friend
Boy/Male
Tamil
Satyachander | ஸதà¯à®¯à®¾à®šà®¾à®¨à¯à®¤à¯‡à®°Â
Truth
Satyachander | ஸதà¯à®¯à®¾à®šà®¾à®¨à¯à®¤à¯‡à®°Â
Surname or Lastname
English
English : from Middle English reuthe ‘pity’ (a derivative of rewen to pity, Old English hrÄ“owan) nickname for a charitable person or for a pitiable one. The personal name Ruth was little used in England in the Middle Ages among non-Jews, and is unlikely to have had any influence on the surname.Swiss German : from a short form of any of the Germanic personal names formed with hrÅd ‘renown’ (see Rode).
Boy/Male
Hindu
Truth
Girl/Female
Christian & English(British/American/Australian)
Friend to All
Girl/Female
Hebrew
Companion; friend; vision of beauty. In the Bible, Ruth the Moabitess was the great grandmother...
Boy/Male
Gujarati, Hindu, Indian, Tamil, Telugu
Lord of Truth; Truth
Boy/Male
Sikh
Boy/Male
Hindu, Indian, Portuguese
Nice
Surname or Lastname
English (West Midlands)
English (West Midlands) : nickname from Middle English trowthe, trouthe ‘good faith’, ‘loyalty’. By my troth was a common phrase emphasizing the veracity of an assertion, and the nickname may have been bestowed on someone who used it habitually or to excess.
Girl/Female
Tamil
Truth
Girl/Female
Tamil
Yathartha | யதாரà¯à®¤
Truth
Yathartha | யதாரà¯à®¤
Boy/Male
Gujarati, Hindu, Indian
Earth
Boy/Male
Tamil
Satyaraj | ஸதà¯à®¯à®¾à®°à®¾à®œ
Truth
Satyaraj | ஸதà¯à®¯à®¾à®°à®¾à®œ
Girl/Female
Tamil
Yognya | யோகà¯à®¨à¯à®¯à®¾
Truth
Yognya | யோகà¯à®¨à¯à®¯à®¾
Boy/Male
Hindu
Wind
Boy/Male
Indian, Punjabi, Sikh
Seeker of Source
TRUTH TABLE
TRUTH TABLE
TRUTH TABLE
TRUTH TABLE
TRUTH TABLE
TRUTH TABLE
TRUTH TABLE
a.
Truth; reality.
n.
A true thing; a verified fact; a true statement or proposition; an established principle, fixed law, or the like; as, the great truths of morals.
n.
The quality or being true; as: -- (a) Conformity to fact or reality; exact accordance with that which is, or has been; or shall be.
n.
The practice of speaking what is true; freedom from falsehood; veracity.
n.
Truth; verity; veracity; as, by my troth.
a.
Observant of truth; habitually speaking truth; truthful; as, veracious historian.
n.
That which is true or certain concerning any matter or subject, or generally on all subjects; real state of things; fact; verity; reality.
v. t.
To assert as true; to declare.
n.
Truth.
n.
Conformity to rule; exactness; close correspondence with an example, mood, object of imitation, or the like.
n.
Truth.
n.
One who tells the truth.
a.
Truth-telling; truthful; veracious.
pl.
of Truth
a.
Speaking truth; truthful.
n.
Fidelity; constancy; steadfastness; faithfulness.
n.
Righteousness; true religion.
n.
Credibility or truth.
n.
One who loves the truth.
n.
Truth; reality.
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