Modern computers based on "ancient" electronic computers, as the basic principles of operation are based on certain postulates.They are called the laws of algebra of logic.The first such discipline has been described (certainly not as detailed as in its present form) ancient Greek scientist Aristotle.
Presenting a separate branch of mathematics in which we study the propositional calculus, algebra, logic has a number of well-aligned findings and conclusions.
In order to better understand the subject, analyze concepts that will help in the future to learn the laws of algebra of logic.
Perhaps the main term in the study discipline - statement.This kind of statement that can not be both true and false.He has always characterized by only one of these characteristics.This conditionally accepted the truth to give a value of 1, falsity - 0, and call itself a statement of some Latin letter: A, B, C. In other words, the formula A = 1 means that the proposition A is true.With statements can come in many different ways.Briefly consider the actions that you can do with them.We note also that the laws of algebra of logic it is impossible to learn without knowing the rules.
1. disjunction of two statements - the result of the operation "or".It may be either false or true.It uses the symbol «v».
2. Conjunction. result of such acts committed with two statements, will be a new statement true only if both statements are true source.Use the "i" symbol "^".
3. implication. Operation "if A, then B".The result is a statement, a false only if the truth of A and B. It is used falsity symbol «- & gt;».
4. The equivalence.Operation «A if and only if B when".This statement is true when both variables have the same assessment.It uses the symbol «& lt; - & gt;».
There is also a series of operations, similar to the implication, but in this article, they will not be considered.
now consider in detail the basic laws of algebra of logic:
1. The commutative and commutative states that a change in the terms of Logical operations conjunctions or disjunctions in the result has no effect.
2. associative or associative.According to this law, the variables in the operations of conjunction and disjunction can be grouped.
3. Distribution or distribution.The essence of the law is that the same variables in the equations can be factored out without changing the logic.
4. The law of de Morgan (inversion or denial).Denying operations is equivalent to the conjunction of disjunction negation of the original variables.Denial of the disjunction, in turn, is equal to the conjunction of the negation of the same variables.
5. Double Negative.The denial of a statement results in twice the original statement three times - its negation.
6. idempotency Act as follows for the logical addition: xvxvxvx = x;for multiplication: x ^ x ^ x ^ = x.
7. The law of non-contradiction states: two statements if they are contradictory, at the same time can not be true.
8. The law of excluded middle.Among the two contradictory statements one - always true, else - false, no middle ground.
9. The law of absorption can be written in such a way to logical addition: xv (x ^ y) = x, for multiplication: x ^ (xvy) = x.
10. Law bonding.Two adjacent conjunctions are able to stick together, forming a conjunction of lower rank.When this is the variable, in which the original conjunction glued disappears.Example for logical addition:
(x ^ y) v (-x ^ y) = y.
We have considered only the most common laws of algebra of logic, which in fact can be a lot more, as is often the logical equations acquire long and ornate appearance, which can be cut by applying a number of similar laws.
As a rule, for the convenience of counting and identifying the results using special tables.All existing laws of the algebra of logic, the table which has the general structure of the grid rectangle painted by distributing each variable in a separate cell.The greater the equation, the easier to cope with it by using the table.
