The concept "Table of the Validity" is closely connected with logical functions, in these functions the variables can accept only logical values – 0 and 1. Logical functions can be set by means of tables of the validity, at the same time the table consists of arguments of function and its values at these arguments. At creation of tables of the validity it is necessary to consider an order of performance of logical operations.
Instruction
1. From an algebra course the logician the main operations over logical expressions, an order of their performance following are known: 1. inversion; 2. conjunction; 3. disjunction; 4. implication; 5. equivalence. The sequence of operations can be changed by means of brackets.
2. The table of the validity for difficult expression is under construction on the following algorithm: 1. The quantity of lines on a formulekolichestvo of lines = 2^n + a line for heading where n is the number of simple statements, 2 is defined. The quantity of columns on a formulekolichestvo of columns = quantity of variables + the number of logical operations, 3 is defined. The table is under construction and is filled with results of operations in the above-stated sequence, at the same time the table of the validity of simple logical operations is used.
3. For example, we will take it vyrazheniyed = to A & (B U C).1. At expression there are statements of A, B and C, thus, of n = 3, a sootvetstvennokolichestvo of lines = 92. Intermediate results: • to And – inversion, we will designate it by the letter E · B U C – a disjunction, we will designate it by letter F • D = to A & (B U C) = E & F – konjyunktsiya3. Thus, the table of the validity will take the form shown in the drawing.