Which of the following sentences are statements? Give reasons for your answer.
(i) There are 35 days in a month.
(ii) Mathematics is difficult.
(iii) The sum of 5 and 7 is greater than 10.
(iv) The square of a number is an even number.
(v) The sides of a quadrilateral have equal length.
(vi) Answer this question.
(vii) The product of (–1) and 8 is 8.
(viii) The sum of all interior angles of a triangle is 180°.
(ix) Today is a windy day.
(x) All real numbers are complex numbers.
The negation of this statement is:
It is false that is not a complex number. Or
is a complex number.
The negation of this statement is:
It is false that Chennai is the capital of Tamil Nadu. Or
Chennai is not the capital of Tamil Nadu.
Give three examples of sentences which are not statements. Give reasons for the answers.
(i) ‘Yesterday was Sunday’.
This sentence is correct (true) on Monday but not on other day.
Hence, it is not a statement.
(ii) ‘She is a doctor’.
This sentence is not a statement because who ‘she’ is.
(iii) ‘sin θ is always greater than 0’.
It is not a statement because one cannot say anything about the value of sin θ without knowing the value of θ .