El programa está destinado a obtener tablas de verdad de funciones lógicas con el número de variables de uno a cinco. Una lógica (Booleano) función de n variables y = f(x1, x2, ..., xn) is a function with all variables and the function itself can take only two values: 0 and 1.

The basic functions of logic

Variables that can take only two values 0 and 1 are called logical variables (or just variables). Note that a logical variable x can imply under number 0 some statement which is false, and under number 1 some statement which is true.

It follows from the definition of a logical function that a function of n variables is a mapping Bn to B, which can be defined directly by a table called the truth table of this function.

The basic functions of logic are functions of two variables z = f(x,y).

The number of these functions is 24 = 16. Let us renumber them and arrange them in the natural order.

Let us consider these functions in more detail. Two of them f0 = 0 and f15 = 1 are constants. The functions f3, f5, f10 and f12 are essentially functions of one variable.

The most important functions of two variables have special names and designations.

1) f1 – conjunction (AND function)
Note that the conjunction is actually the usual multiplication (of zeros and ones). This function is denoted by x&y;

2) f7 is a disjunction (or function). It is denoted by V.

3) f13 is implication (following). Denoted by ->.
This is a very important function, especially in logic. It can be viewed as follows: if x = 0 (i.e. x is “false”), then both “false” and “true” can be deduced from this fact (and this will be correct), if y = 1 (i.e. y is “true”), then truth is deduced from both “false” and “true”, and this is also correct. Only the conclusion “from truth is false” is incorrect. Note that any theorem always actually contains this logical function;

4) f6 – addition modulo 2. It is denoted by a “+” sign or a “+” sign in a circle.

5) f9 is equivalence or similarity. This f9 = 1 if and only if x = y. It is denoted by x ~ y.

6) f14 is Schaeffer’s dash. This function is sometimes called “not and” (since it is equal to the negation of the conjunction). It is denoted by x|y.

7) f8 is Pierce’s arrow (sometimes this function is called the Lukasiewicz stroke).

The remaining three functions, (f2 , f4, and f11) have no special designation.

Note that logic often considers functions from functions, i.e., superpositions of the above functions. In this case, the sequence of actions is indicated (as usual) by parentheses.

User manual

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