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Consider the following sentences:
  1. Chennai is the capital of Tamil Nadu.
  2. 2 + 3 = 6.
  3. Read this carefully.
  4. .
  5. go for it.
  6. 10 is a positive integer.
Let us analyse the following sentences:
  1. It is a true statement.
  2. It is false.
  3. We cannot say anything about this sentence, because it is only an instruction.
  4. It may or may not be correct as we do not know anything about .
  5. It is a command.
  6. It is true.
A sentence is a mathematically acceptable statement if it is either true or false but not both. Going by this definition, we can say that 1, 2, 6 are statement 3, 4, 5 are not statements.

Let us consider few more examples

Example 1:

Check if the following are statements:
  1. Moon is a star.
  2. 5 is a prime number.
  3. This month has 30 days.
  4. How old are you?
  5. 1998 was a leap year.
  1. According to established facts moon is a satellite of the earth. So we know that this sentence is false.Hence it is a statement whose truth value is false.
  2. 5 is a prime number, which is true. Hence it is a statement which is true.
  3. “This month has 30 days”; does not tell us clearly which month is referred to therefore it is not a statement.
  4. It is a question and hence not a statement.
  5. It is a statement even though it is false.
Example 2:
Give 3 examples each for
  1. statements which are true
  2. statements which are false
  3. sentences which are not statements
Given reason for your answers.

  1. Statements which are true are as follows:
    1. 3 + 3 = 6
      It is a true statement
    2. The population of India is 100 crores.
      It is a statement because we know the population of India is about 100 crores. So the statement can be treated as true. If it is not exactly 100 crores, it is false. Either way it is a statement.
    3. 2009 is not a leap year
      It is a true statement
  2. Statements which are false are as follows:
    1. Thirupathi is in kerala.
      We know that Thirupathi is in Andhra Pradesh and so it is a false statement.
    2. 1 is a prime number.
      We know that “1” is not a prime. So it is false statement
    3. May is a winter month in Tamil Nadu
      We know that the month of May belongs to summer in Tamil Nadu. So it is a false statement.
  3. Sentence which are not statements are as follows:
    1. Girls are smarter than boys.
      This can be an opinion of some people; but need not be true or false.
    2. is greater than .
      Truth value of the sentence can be decided with the knowledge of .
    3. "Bring that book"
      It is not a statement as it is a command which has no truth value.

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