Equivalence table, example of solving a logical problem with an operation of equivalence

Today we propose to talk about logical functions. We give an equivalence table, since this is our main question.

In Boolean algebra, you do not need to memorize rules and truth tables at all, just a simple understanding of the essence of the function that is presented to you will suffice.

Logics

Despite the fact that the question of the equivalence table is a priority, we will say a few words about Boolean algebra itself. As already mentioned, truth tables should not be learned as a multiplication table. To understand the essence of the operation, you can give an example from the Russian language. However strange it might seem, this method really helps many to overcome the barrier, turning the computation of logical tasks into an interesting activity. Today you can see how this method works.

Why do we need logic? This science is very important, especially in our time. Almost all digital devices that we use on a daily basis are based on logical operations. Even if you do not touch on the technical side, pay attention to how you talk. All your proposals must obey the laws of logic as well as flying from the ninth floor down the ball obeys the laws of physics.

Functions

The Boolean algebra contains several basic functions (negation, multiplication, addition, consequence and equivalence).

Note that the condition for a complex logical expression does not contain terms such as "multiplication" or "addition", it is necessary to remember their correct definitions. Negation is called inversion. Multiplication in a Boolean algebra is called a conjunct, and addition is a disjunction. The logical consequence is implication. Equivalence is sometimes called equivalence.

To solve logical problems, you simply need to know the truth tables of these functions. But we have already said that you can not learn it, but UNDERSTAND. This will greatly reduce the costs of your time. We will test this method on the table of equivalence. Let's start right now.

Equivalence

A logical function that is true only if both input expressions are equivalent, this is the equivalence. The function whose table will be listed below is a two-place logical operation. Graphically, it is indicated by either a two-sided arrow or three horizontal lines. The sign must separate two simple expressions.

If we consider the priority of functions, then this logical operation takes the sixth place, yielding to all the others. Below is the table of equivalence.

Note that the truth table can be populated in several ways. The true expression can be written as: "+", "1" or "AND". False - "-", "0" or "L".

As we promised, we interpret this logical operation in Russian. The expression will be true in the following cases:

• The first simple expression is the same as the second expression (the expression is a phrase);
• The first expression is equivalent to the second (my education is equivalent to education in Britain);
• An expression at number one is possible if and only if there is a place for the second (I will enter the university if and only if I graduate from school).

Example

Now let's try to use the equivalence truth table in practice. It is necessary to prove that the two expressions below are equivalent:

• Expression 1 is equivalent to 2;
• (1 + not 2) * (not1 + 2).

To do this, we will compile truth tables for these statements. For the first, we will not do, since we have it in the previous paragraph.

Note that the last results in the last column are identical, hence, the expressions are equivalent.