Conclusion Mathematical Logic

To bear witness the novel declaration or proof, the truth must survive shown every bit a resultant of to a greater extent than or less other grouping of statements, each of which may survive accepted every bit truthful or previously verified. The revelations received past times the truth without needing proof are called axioms. For example, "Two unlike lines tin forcefulness out non intersect at to a greater extent than than ane point".

In proving a proffer or deriving an resultant of the known truths the argumentation blueprint is used, namely past times drawing conclusions from known statements called premises based on logical principles, namely ponen mode, tollens means as well as syllogism.

Conclusions are said to survive legitimate, if the conjunctions of the premises stimulate got concluded implications. Conversely, if the conjunctions of the premises stimulate got no implication as well as so the declaration is said to survive imitation or illegitimate. Thus, a decision is said to survive valid if the premises are truthful as well as so the conclusions are likewise true.

1. Ponen mode

The ponen means is an declaration inward the shape of the following:

"If p → q is truthful as well as p is truthful as well as so q is true"

In the shape of diagrams tin forcefulness out survive presented every bit follows:

Example of Ponen Mode

Premise 1: If a kid diligently learns, as well as so he passed the test
Premise 2: Ahmad is a diligent child
Conclusion: ∴Ahmad passed the exam

To bear witness valid or non parse-drawing inference tin forcefulness out survive used truth table. Ponen means declaration "If p → q is truthful as well as q is truthful as well as so q is true" tin forcefulness out survive written inward the shape of implication, that is:

[(p → q) ∧ q] → q

This decision is said to survive valid if it is a tautology. The truth tabular array of the shape is every bit follows:

Information :
T : True
F : False

From the tabular array to a higher house it appears that [(p → q) ∧ q] → q is a tautology. So the declaration or decision of the ponen means shape is valid.

2. Tollens mode

The tollens means is an declaration inward the shape of the following:

"Jika p → q benar dan q benar maka p benar"

In the shape of diagrams tin forcefulness out survive presented every bit follows:

Example of Tollens Mode

Premise 1: If it is Sunday, as well as so Budi is on an excursion
Premise 2: Budi is non on an excursion
Conclusion: ∴ it is non Sunday

To bear witness valid or non decision past times tollens means tin forcefulness out survive used truth table. Ponen means declaration "If p → q is truthful as well as q truthful as well as so p is true" tin forcefulness out survive written inward the shape of implication, that is:

[(p → q) ∨ q] → q

This decision is said to survive valid if it is a tautology. The truth tabular array of the shape is every bit follows:

Information :
T : True
F : False

From the tabular array to a higher house it appears that [(p → q) ∨ q] → q is a tautology. So the declaration or decision of shape tollens means is valid.

3. Silogism

Silogism is an declaration shaped every bit follows:

"If p → q is truthful as well as q → r is truthful as well as so p → r is true"

In the shape of diagrams tin forcefulness out survive presented every bit follows:

Example of Silogism

Premise 1: If you lot written report hard, as well as so you lot acquire to class
Premise 2: If he goes to class, he volition purchase a bicycle
Conclusion: ∴If you lot written report hard, you lot volition purchase a bicycle

To bear witness valid or non silogism decision tin forcefulness out survive used truth table. The silogism declaration "If p → q is truthful as well as q → r is truthful as well as so p → r true" tin forcefulness out survive written inward the shape of implication, that is:

[(p → q) ∧ (q → r)] → (p → r)

This decision is said to survive valid if it is a tautology. The truth tabular array of the shape is every bit follows:

Information :
T : True
F : False

From the tabular array to a higher house it appears that [(p → q) ∧ (q → r)] → (p → r) is a tautology. So the declaration or decision of the silogism shape is valid.

The decision does non depend on the fairness or non the pregnant of the decision every bit a declaration only on the truth value of the conclusion.

• Arguments whose conclusions are meaningful only are non obtained past times using logical principles, as well as so the conclusions are invalid.
• Some of the arguments to which the conclusions are odd only are obtained past times using the principles of logic thus the conclusions are valid.

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Sorry if in that place is a incorrect word.
The halt of give-and-take wassalamualaikum wr. wb

Referensi :

• To'Ali's mass math grouping accounting as well as sales