A truth table is a mathematical table used in logic and can be used to see if a logical proposition is true for any input value. Truth tables are primarily used in connection with boolean algebra, boolean functions, and propositional calculus. A truth table has one column for each input variable, e.g. A and B and a row for each possible combination of the input variables being true and false. Other columns are then added for each logical operator such as “And”, “Or” and “XOR” and the results of these operators for each combination of inputs.
Technipages Explains Truth Table
The Austrian philosopher Ludwig Wittgenstein is generally credited with inventing and popularising the truth table in a book published in 1921, although another philosopher Charles Sanders Peirce has since been discovered to have invented them in 1893 in a manuscript that was never published.
There are 16 possible operations that can be performed over two true or false variables. These operations are: Contradiction – this is always false; Logical NOR – only true when neither A nor B are true; Converse nonimplication – is true where B is true and A is false; Negation – is only true when A is false, no matter the value of B; Material nonimplication – is true when A is and B is not; Negation – Exclusive disjunction; Logical NAND; Logical conjunction; Logical biconditional; Projection function; Material implication; Projection function; Converse implication; Logical disjunction and Tautology.
Each of them has their own uses and purposes of course, but they have one thing in common: They are performed with the use of one or two true/false variables. Due to the simple (if not easy to understand) nature of these variables and operations, it’s possible to break complicated operations down into a small set of elements – true/false values and the above operations.
Common Uses of Truth Table
- A truth table is a mathematical table used in logic.
- Each row of the truth table contains one possible configuration of the input variables.
- Truth tables can be used to prove logical equivalences.
Common Misuses of Truth Table
- Truth tables check if data in a table or database is correct.