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A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. [1]
Boolean logic allows 2 2 = 4 unary operators; the addition of a third value in ternary logic leads to a total of 3 3 = 27 distinct operators on a single input value. (This may be made clear by considering all possible truth tables for an arbitrary unary operator.
The left figure below shows a binary decision tree (the reduction rules are not applied), and a truth table, each representing the function (,,).In the tree on the left, the value of the function can be determined for a given variable assignment by following a path down the graph to a terminal.
In mathematics and mathematical logic, Boolean algebra is a branch of algebra.It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.
We build a table consisting of columns and + rows, where N is the number of variables in the function. In the top row of the table we place the vector of function values, that is, the last column of the truth table. Each row of the resulting table is divided into blocks (black lines in the figure).
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.
The idea behind the logic alphabet is to first represent the sixteen binary truth functions in the form of a square matrix rather than the more familiar tabular format seen in the table above, and then to assign a letter shape to each of these matrices. Letter shapes are derived from the distribution of Ts in the matrix.
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [ 1 ] and the LaTeX symbol.