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

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

In Boolean algebra, there is absolutely no need to memorize the rules and truth tables; 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 the Boolean algebra itself. As already mentioned, truth tables should not be memorized as a multiplication table. To understand the essence of the operation, we can give an example from the Russian language. It may seem strange, but this method really helps many to overcome the barrier, turning the calculation of logical tasks into an interesting lesson. Today you can see how this method works.

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

Functions

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

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

To solve logical problems, you just need to know the truth tables of these functions. But we have already said that you can not memorize it, but UNDERSTAND. This will significantly reduce the cost of your time. We will try this method on the equivalence table. Let's get started right now.

Equivalence

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

If we consider the priority of functions, then this logical operation takes sixth place, giving way to all others. The following is an equivalence table.

Please note that the truth table can be filled 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 (expression is a phrase);
• the first expression is equivalent to the second (my education is equivalent to education in Britain);
• expression number one is possible if and only if there is a place for the second (I will go to university if and only when I finish school).

Example

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

• expression 1 is equivalent to expression 2;
• (1 + non2) * (non1 + 2).

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

Please note that the last results in the last column are identical, therefore, the expressions are equivalent.