TopIn mathematics, if we cannot identify that the given sentences are true or false, than this type of sentence is called as an Open Sentences if ‘n’ is an even number, then we cannot say that ‘n’ is an even number or an odd number. So, there is no surety of true or false in that sentence. Therefore this sentence is an open sentence. There are following type of open sentences -

Relational open sentences: An open sentence, which have relational operators are called as a relational open sentences like 2 + 4y < 6.

Arithmetic open sentences: Open sentences, which have arithmetic operators like addition, subtraction, multiplication and division, are called as arithmetic open sentences,

Like x + 3 = 8.

Now we discuss how we solving open sentences:

For solving open sentences, we use following steps -

Step 1: First of all, we check what kind of open sentences we have like we have relational open sentences or we have arithmetic open sentences.

Step 2: In relational open sentences, we use number line to perform these open sentences like for solving the 2 + 4y < 6, we simplify the equation -

2 + 4y < 6,

=> 4y < 6 – 2,

=> 4y < 4,

=> y < 1,

Now we make number line for y < 1, means all number less than 1 on number line are answer of these open sentences.

Step 3: For solving the arithmetic open sentences, we put value, if it satisfy the equation, then our open sentences are true unless it is a false sentence like we have an open sentence, x + 3 = 8.

Now we solve this equation -

x + 3 = 8,

=> x = 8 – 3,

=> x = 5,

Now we check true or false -

x + 3 = 8,

Now put x = 5

=> 5 + 3 = 8 = r h s

So, l h s = r h s

Therefore x + 3 = 8 is an open sentence, which produces true result for x = 5.