Simple and Compound Propositions

Content

• Prayer or proposition?
• Types of propositions
• Simple propositions
• Compound propositions
• Examples of simple propositions
• Examples of compound propositions
• Propositions in the formal sciences

A proposition it is a statement with complete meaning, and constitutes the most elementary form of logic. The propositions provide information about a falsifiable event, that is, it can be false or true. For example: The earth is flat.

Propositions are the basic elements from which reasoning is built and that is why they were widely used in the field of science and epistemology.

• It can help you: Simple and compound sentences

Prayer or proposition?

In many times, the concept of proposition is confused with that of sentence or statement. The sentence is a grammatically composed linguistic expression that expresses a thought or an opinion, while a proposition is an idea rather related to logic, which necessarily has a subject concept that fulfills the function of determining the object.

The propositions almost always have the verbs "ser" or "estar" to refer to a permanent or provisional state of affairs.

Types of propositions

There are different criteria for classifying propositions:

• Universal / particular. According to Aristotle, there are universal propositions, in which a state is generalized for every element that meets a characteristic, and particular propositions, when the subject is taken from its particular extension.
• Negative / positive. They express a state of situation (the positive ones) or the very absence of that state (the negative ones).
• Simple / compound. Compound propositions are the most extensive and complex, while simple propositions are the shortest and most direct, generally containing a subject, an object and the verb "is".

Simple propositions

The simple propositions are those that express a state of affairs in its simplest state, that is, linking a subject with an object from the verb "is". They exist both in the field of mathematics and in other disciplines and are characterized by not having any term that conditions the proposition in any way. For example: The wall is blue.

Compound propositions

The compound propositions appear mediated by the presence of some kind of connector, which can be oppositional (or, nor), addition (and, e) or condition (yes). Furthermore, negative propositions, which include the word no.

This explains that in the compound proposition the relationship between the subject and the object does not occur in a general way, but is subject to the presence of the connector: it can be fulfilled only when something else happens, it can be fulfilled both for him and for others, or it can be fulfilled just for one of all.

Examples of simple propositions

1. 9 and 27 are factors of 81.
2. That box is made of wood.
3. Nothing is forever.
4. Classical music is the oldest in the world.
5. Even numbers are divisible by two.
6. The capital of Russia is Moscow.
7. That girl is my friend.
8. It's three in the afternoon, twenty-six minutes.
9. Carnivorous animals eat plants. (False proposition)
10. My name is Fabian.
11. It's raining.
12. The number 1 is a natural number.
13. In this country, summer is very hot.
14. Tomorrow will be Wednesday.
15. The number 6 is less than the number 17.
16. Today is October 7.
17. His cat is brown.
18. My brother sells pasta.
19. The earth is flat.
20. Mario Vargas Llosa is an important writer.

Examples of compound propositions

1. I can drive a car if it has power steering.
2. Gabriel García Márquez was a great writer and dancer.
3. Cells are prokaryotic or eukaryotic.
4. The square root of 25 is 5, or -5.
5. Not all prime numbers are odd.
6. My brother-in-law is an architect and an engineer.
7. Tech gadgets are black, white, or gray.
8. If I'm hungry then I cook.
9. Turkey is a country that is located in Asia and Europe.
10. The sum of the squares of both legs is equal to the square of the hypotenuse, if it is a right triangle.
11. A whale is not red.
12. The largest number is not 1,000,000.
13. If the sheep eats grass, it is herbivorous.
14. If the information is not complete for bidders and applicants, there is a market failure.
15. It's raining and it's hot.
16. Our flag is white and blue.
17. 9 is a divisor of 45, and 3 is a divisor of 9 and 45.
18. Marcos is dedicated to swimming or mountaineering.
19. The number 6 is greater than 3 and less than 7.
20. I have spent all my vacations in Greece and Morocco.

Propositions in the formal sciences

The question of propositions is fundamental in the field of formal sciences, among which mathematics stands out. Although what is usually seen of it are numbers, operations and equations, deep down everything is supported by demonstrations, which are made with propositions that must be founded.

A set of propositions constitutes a proof when it is interrelated with a series of axioms, rules of inference and logical interpretations: the latter is the fundamental task of the mathematician.

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