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Open Sentence|Definition & Meaning
Definition
In the field of mathematics, a “sentence that employs variables,” also known as a “statement that includes letters to express an unknown number,” is referred to as an “open sentence.” Given that a variable represents an undetermined quantity, it cannot be determined if the opening line is true or untrue. This is why it is known as open; the possibility remains open as to whether or not the assertion works.
What Is a Sentence in Math?
The concept of a sentence is most commonly associated with the reading and writing processes; nevertheless, sentences can also be found in mathematical discourse. A mathematical sentence, like a sentence in reading or writing, conveys a whole notion. There is, without a doubt, a distinction that can be made between the two.
Can you explain what a math sentence is? A mathematical sentence concludes or offers a comparison between two expressions. A math sentence can mean various things depending on the context. It can use words, numbers, variables, or any combination.
Figure 1: Representation of a sentence
Equations are mathematical statements that compare two expressions using a symbol known as the equal sign (=). An inequality is another mathematical phrase that compares two expressions using a symbol that denotes the inequality, such as larger than or less than (> or <). Take, for instance:
5 x 3 = 15
2 x 2> 2 x 1
7 + 21 < 10 x 4
A comparison of two expressions is what a math sentence does, as was mentioned earlier. It can be either true or untrue, open or closed.
What Is Meant by Open-sentence Math?
In the field of mathematics, a “sentence that employs variables,” also known as a “statement that uses the letter to express an unknown number,” is referred to as an “open sentence.” Given that a variable represents an undetermined quantity, it cannot be determined if the opening line is true or untrue.
This is why it is known as open; the possibility remains open as to whether or not the assertion works. When looking at a mathematical sentence, the first thing you should do is determine whether or not there are any variables. If there is, we are dealing with an open mathematical statement.
Figure 2: Diagrammatic representation of a sentence
If you need to write open mathematical sentences, you need to make sure that a variable is used anywhere in the sentence. Any one of the following could be considered an example of an open sentence:
- The answer to the equation for finding the square root of 4 is n
- 2x + 3y = 24
- n is a number that is less than 40
- 124 – y = 84
- x is an odd number.
If the value for the variable is either given or calculated, then and only then can it be determined if the assertion being tested is true or false. For example, the previous illustration stated that the number x is an odd integer. If it is established that x = 14, then it may be deduced that the assertion is untrue because 14 is an even number; instead, 14 is an even number.
If it were said that x = 11, then the phrase would be accurate because 11 is, in fact, an odd number. This would be the case if it were stated that x = 11.
The answer to your question is that the square root of 4 is n. It was found that n equals 2 by calculating the square root of 4. Consequently, if the letter n in that sentence were changed to the number 2, such that it read “the square root of 4 is 2,” then the assertion would be accurate.
If any other number were used instead of 8, for example, the assertion would be invalid since it cannot be true that the square root of 4 is 2. This cannot be proven using mathematics.
What Is Meant by the Term “Closed Sentence?”
Contrary to this, a closed sentence is one in which the answer to the question it poses is already known. In a sentence with no gaps, there is no room for speculation and no variables or uncertain components. Because each component of both statements is stated unequivocally, determining whether or not it is correct may be done with relative ease.
Make sure there are no variables involved and that a complete mathematical expression is utilized on both sides of the equals sign or the inequality symbol when attempting to compose a closed sentence.
What Exactly Is Meant by an “Open Formula?”
A formula that only calls for one variable to be entered is said to be open. The criterion is for at least one variable. However, it is possible for there to be more than one. In contrast to a closed formula, which defines a proposition and can therefore have a truth value such as true or false, an open formula does not have an objective truth ascribed to it.
Students will begin by learning arithmetic phrases to determine whether or not a statement is true or untrue; even algebraic expressions can be written in the form of aspen sentences.
Math is a subject in which all of the themes need to be learned with the appropriate perception, and one more thing that needs to be kept in mind is that it cannot be learned in a day or two. It is a slow process that goes on indefinitely.
Figure 3: Symbols used in a sentence
Students must develop effective study strategies and put those skills into practice daily. The more you put in the effort to practice, the deeper your comprehension will get.
Example 1
a + 5 = 7
What is the value of a?
Solution
By substituting a = 1 in the above equation, the answer will be 6, which is smaller than 7.
1 + 5 = 6
Thus, this sentence is false.
Now, by substituting a = 2 in the above equation, the answer will be 7.
2 + 5 = 7
Thus, this sentence is true.
Example 2
1.7x = 6.8
What is the value of x?
Solution
By putting x = 4, the answer is equal to 6.8.
1.7 (4) = 6.8
So, it is true when x = 4.
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