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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.


(i) This sentence is false because the maximum number of days in a month can never exceed 31. Hence, it is a statement.
(ii) This sentence is neither true nor false because Mathematics can be easy for some people and can be difficult for some others. Hence, it is not a statement.
(iii) 
This sentence is true because the sum of 5 and 7 is 12 which is greater than 10.Hence, it is a statement.
(iv) This sentence is false as square of odd number is odd and square of even number is even. Hence, it is a statement.
(v) 
This sentence is sometimes true and sometimes false, e.g., squares and rhombus have equal sides, whereas rectangles and trapezium have unequal sides. Hence, it is not a statement.
(vi) This sentence is an order. Hence, it is not a statement.
(vii) This sentence is false as the product of (-1) and 8 is -8. Hence, it is a statement.
(viii) This sentence is always true. Hence, it is a statement.
(ix) It is not clear from the context which day is referred. Hence, it is not a statement.
(x) This sentence is true as every real number a can be written as a + i (0). Hence, it is a statement.


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Write the negation of the following statement:
square root of 2 is not a complex number.

The negation of this statement is:
It is false that square root of 2 is not a complex number.   Or
square root of 2 is a complex number.

487 Views

Write the negation of the following statement:
Chennai is the capital of Tamil Nadu.

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.

243 Views

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 .

482 Views

Write the negation of the following statement:
All triangles are not equilateral triangle.

The negation of this statement is:
It is false that all triangles are not equilateral triangles.  Or
All triangles are equilateral triangles.

324 Views

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