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A truth table or a logic table is a table for determining the true or false statement of a compound statement. Each statement is depicted by a variable or a letter such as p, q, or r. Each statement also consists of a column with all the truth values. The logical reasoning that truth tables are built from can be used to evaluate the truth or false nature of the statement. Logical reasoning can be used to evaluate whether the statement’s nature is true or false, or maybe, in this case, it can be used to make backup plans.
Unary Operations Truth Tables
The logic table is a valuable concept that constructs the table for the statement components. Unary logical operations consist of only one logical variable.
Logical True Truth Table
Truth value is returned by Logical true for every input.
The truth table is as follows:
P | T(P) |
T | T |
F | T |
Logical False Truth Table
A false value is given by Logical false for the input. The truth table goes by
P | T(P) |
T | F |
F | F |
Negation Truth Table
The unary operation named Logical negation depicts the value opposite to the proposition. A false input depicts output as true and vice versa. It is represented by or, ~p, NOT. The logic table is as follows:
P | ∼P |
T | F |
F | T |
Truth Tables for Binary Operations
are logical operations; it consists of two logical input variables. The logic tables are the most viable binary operations as stated below:
Conjunction Truth Table
The conjunction is a binary logical operation that depicts the true value if both values pertaining to the input are true. The operator is signified by P & Q, P, AND Q, P ∧ Q, or P . Q. In this, P and Q are known as input variables. The truth table goes as follows:
P | Q | P ∧ Q |
T | T | T |
F | T | F |
T | F | F |
F | F | F |
Implication Truth Table
Implication interprets a false value in a single case that the first input is true and the other is false or may be true. It is linked with the condition if P then Q as a statement condition and is denoted as P ⇒ Q or P → Q . Logic value goes an as follows:
P | Q | P → Q |
T | T | T |
F | T | T |
T | F | T |
F | F | T |
Disjunction Truth Table
A Logical disjunction is said to be true if one input value is true, which means either one is true or both are true.
The denotation can be done by several symbols such as P + Q, P V Q, P OR Q. Truth tables goes as follows:
P | Q | P ∨ Q |
T | T | T |
F | T | T |
T | F | T |
F | F | F |
Bi-conditional truth table
P ↔ Q equivalence or bi-conditional truth table is the truth value if both the input variables are true QR and P and Q are false. It can be linked to one conditional statement P if only if Q and its denotation by P. Truth table go as follows:
P | Q | P ↔Q |
T | T | T |
F | T | F |
T | F | F |
F | F | T |
Tables for Logic and Truth
In these operations between logic tables with truth tables. The standard truth tables are propositional logic truth tables. So the propositional value cannot be changed.
Logical NAND
NAND is a binary logical operation identical to implementing NOT on AND operation. Furthermore, NAND produces a true value if one of the input variables is false. The denotation is by P | Q, P NAND Q, or P ↑ Q. The table is as follows:
P | Q | (P ∧ Q) And |
T | T | F |
F | T | T |
T | F | T |
F | F | T |
Logical NOR
This is a logical operation attained by implementing a NOT on an OR operation. It results in NOR into true value if both input variables are false. The representation by the logical NOR is a logical operation that is obtained by applying a NOT operation to an OR operation. We cannot say that NOR results in a true value if the input variables are false. It is represented by P ↓ Q, P NOR Q. The table is as follows:
P | Q | (P ∨ Q) OR |
T | T | F |
F | T | F |
T | F | F |
F | F | T |
Conclusion
A truth table or a logic table is a part of mathematics that is easy and viable to understand and interpret when it is seen and how its working is conducted than learning it via a definition. In maths, logic or a truth table represents rows and columns depicting the truth value of the combination of the statements in which T stands for true, and F stands for false. The statements are usually represented by an uppercase letter such as P, Q, and R, and logical connectives do operations.
