Definition of Statement, Open Sentence and Settlement Set
Statement, Open Sentence and Its Completion Set - When you want to study the material on the equations and inequalities of a variable, then you should understand the basic material first. The goal is that you can more easily understand the advanced material of the system of equations and linear inequalities of one variable. The basic material in question here is the understanding of statements, open sentences, and the set of solutions. On this occasion The Basic Mathematical Formula will provide one-on-one explanation of these three points. The following is the explanation:
Statement
In the daily life -day of course you often encounter or hear a few sentences like:
1. The size of Papua is bigger than There is the island of Bali.
2. Bandar Lampung is the capital of Lampung province
3. The Eifel Tower is located in France
4. Four smaller than seven (4 <7)
The above sentences are examples of sentences that have true value because everyone would agree that the sentence is true.
Now let's compare with the following sentences:
1. The area of the island of Sumatra is smaller than the island of Bali
2. The capital of the Province of Aceh is Pekanbaru
3. The sun sets in the east
4. Eleven is greater than thirty (11> 30)
The conclusion we can draw from these four sentences is that the sentences are false because it is certain everyone does not agree with those sentences.
Now, from the two examples of the above sentence types we can conclude that the Statement is a sentence whose true value can be determined (false or true).
Now look at some of the following sentences:
1. The beach is beautiful Once
2. The man was really handsome
Can you determine the truth value of the two sentences above? Can the sentences be called statements?
Be aware that these two sentences are not statements. Why is that? Because we can not determine the value of truth. For example in the second sentence "The man is really handsome". Certainly not everyone can approve it, it could be someone thinks he is handsome but others consider the man's face casual. Thus, the phrase whose trueness can not be determined can not be categorized as a statement in mathematics.
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Open sentence
To make it easier to understand what is called an open sentence in mathematics, try Note the following sentence:
"Canada is located on the continent x "
When x is replaced with America, then the sentence can be considered true. However, if x is replaced by Australia, then the value will be wrong. Such a sentence is called an open sentence because its true value depends on its variable.
Let us consider some examples of open sentences in the following mathematical lesson:
1. 7 + x = 12, x is a member of the counting set
2. 8 - y = 5, y is a member of the set of integers
The first sentence can be declared true if x is replaced with number 5 and if x is replaced with a number other than 5 then the statement is false. On the statement x is referred to as variable while 7 and 12 are referred to as constants . Likewise with the second sentence, the sentence would be true if y is replaced with number 3 and if y is replaced with a number other than 3 then of course the sentence will be wrong. In the second sentence the variable is y while the constants are 8 and 5.
Thus, Inside Open sentence we will find Variables and Constants. Variables can be replaced by any given set member. While constants are fixed and can not be replaced.
The set of open sentence settlements
We take the following open sentence example:
[1945909] x 2 = 81
The sentence will be true if we replace the variable X with 9 or -9. Thus, the completion of the open sentence is x = 9 or x = -9. Thus, the settlement set of the sentence x 2 = 81 is 9, -9
Definition of Statement, Open Sentence and Set of Solutions may be useful.
