Tutorial Algebraic Sentence


Algebraic Sentence


   

Algebraic Sentences:
We know that algebraic sentences give relation between two algebraic expressions. For example 2 6 = 8, in this sentence, it is stated that 2 6 and 8 have the same sense.

Following are the few examples of algebraic sentences:
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)

Types of Algebraic Sentences:

  1. Correct Sentences (True Sentences)
  2. Incorrect Sentences (False Sentences)
  3. Open Sentences

Following are the Correct (True) Sentences:
1)
2)
3)
4)
5)
Following are the Incorrect (False) Sentences:
1)
2)
3)
4)
5)
Following are the Open Sentences:
1)
2)
3)
4)
5)
All the above mentioned sentences are such that each one is true for some numerical value but not for all numerical values of variable. For example take . The sentence is true for but not true for any other than 1.
Hence the sentences which are true for some numerical values of variable, but not for all, are called open sentences.

Equations and In-Equalities:
Consider the following open sentences

In (1), (2) and (3) symbol “=” is used. In other cases the symbol “>” or “<” is used.

The sentences in which symbol “=” is used are called equations
And
When the symbol “<” or “>” is used, the sentences are called in-equalities.

e.g. (4), (5) (6) are inequalities.


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