For any logical expression it is possible to construct the table of the validity. This table demonstrates at what values of logical variables the expression addresses in unit or is true. By means of drawing up tables of the validity it is possible to prove equality (or inequality) two difficult logical expressions.
Instruction
1. Count quantity of variables in expression. For n of logical variables it is required 2^n lines of the table of the validity, apart from a line with headings. Then count the number of logical operations in expression. Columns in the table will be as much how many operations plus of n of columns for variables. Let the expression with three variables which is written down in the drawing be given. Variables three therefore lines 8 will be required. The number of operations - 3 therefore the number of columns taking into account variables is equal to 6. Draw the table and fill its heading.
2. Now fill the columns inscribed by names variable, all possible options of variables. To do not pass any option, it is convenient to present for itself these sequences of zero and units in the form of binary numbers from 0 to 2^n. For three variables it is binary numbers from 0 to 8 or from 000 to 111 in a binary numeral system.
3. To begin to fill out the table of the validity most conveniently from filling of results of denial of variables as here it is not required to do any difficult conclusions. In our case it is easy to fill a column of denial of variable B.
4. Then substitute consistently values of variables in the logical operations specified in headings of columns and write down in the corresponding cells of the table, consistently filling out the table.