Notion of Logic - Proposition

VIEW:411 DATA:2020-03-20

When we want to make a logical analysis, we must propose a sentence, that sentence is therefore a proposition. It declares something or affirms, that is, it is an affirmative sentence. And it can only have one of the response values, it is either true or false.

We can see some examples:

The blue house belongs to the group of blue objects. This is a true proposition.

The blue house belongs to the group of red objects. This is a false proposition.

Now, let's replace it with symbols. So let the blue house be the letter c. Be the group of blue objects o A. Be the group of red objects o R.

So we have that "c" belongs to "R" is a false proposition.

And we have that "c" belongs to "A" is a true proposition.

What is that for? This is the basis for the so-called Boolean algebra. All computer systems, cell phones, and any digital electronic systems, use logical link systems. Understanding logic, in addition to assisting in life decisions, helps to understand the functioning of digital devices.

Thus, the blue house does not belong to the group of electronic objects is a true proposition.

The scene ball, does not belong to the group of blue objects, is a true proposition.

The cell phone belongs to the group of electronic objects, it is a true proposition.

Now, that we have already observed the images of objects, we will do our analysis of proposition with numerical sets.

The number 1 belongs to the Natural numbers. This proposition is true.

The number -1 belongs to the Integer numbers. This proposition is true.

The numerical representation of half belongs to Rational numbers. This proposition is true.

The number "Pi" belongs to the Real numbers. This proposition is true.

Now having a basic knowledge of the propositions, let's do some exercises for fixation.

Nine is different from five, so we see that it is a proposition and that it is true.

Seven is greater than three, which is also a true proposition.

We have that two belongs to the whole number. Which is a proposition, and it is true. For two also belong to naturals, and all naturals are within the Integers, so what is natural, is also whole, is also rational, and is also real.

The set of integers are contained in the set of rational numbers. Thus, we saw earlier that the set of simpler numbers are contained in the set of more complex numbers. The symbol between the two sets, is the symbol of contained. We will see later, the sets contained in other sets. So, this proposition is true.

We can organize the numerical sets, in which the Naturals are contained in the Integers, the Integers contained in the Rationals, and the integers contained in the Reais. We will see this later.

But when is something not a proposition? Remember that there are different ways for something not to be a proposition, not to be, is almost always infinitely greater than being, let's just see a few.

Five times seven plus 1. This is not a proposition, because nothing is being said about the core of the sentence. If nothing is said, then nothing can be said. But if it were, five times seven plus 1 equals 36, then we can say that it is true. And then it becomes a proposition.

Pi belongs to Racionais? See that this is a question. I could say that Pi does not belong to Racionais. But a proposition is a statement, in which case it is a question, so a question is not a proposition. For a question cannot be false or true, as it is a doubt. A doubtful person cannot be wrong, nor can he say that he is right, he is just waiting for an answer, which he hopes to be true.

Twice "x" equals 10. "x" is an unknown number. If the "x" is 5 then it is true, but if the "x" is not 5? So wouldn't the proposition be true? Thus, this would not be a proposition. But if I say "x" is equal to 5, then the set becomes a proposition, and that will be true. Any other number, then the proposition will be false. But without these numbers, then it is not a proposition.

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