Class 11 NCERT Solutions – Chapter 14 Mathematical Reasoning – Exercise 14.1

Question 1. Which of the following sentences are statements? Give reasons for your answer?

Note: A sentence is called mathematically acceptable statement if it is either true or false but not both.

(i) There are 35 days in a month.

Solution:

Yes, this is a statement because there can be 28 / 29 / 30 / 31 days in a month but not 35 and therefore this is definitely  false.  

(ii) Mathematics is difficult.

Solution:

No, this is not a statement because for some people math can be easy and for some it is difficult. so it can be both true and false in.  

(iii) The sum of 5 and 7 is greater than 10.

Solution:

Yes, this is a statement because 5 + 7 = 12, which is greater than 10 and therefore this is definitely true.  

(iv) The square of a number is an even number.

Solution:

No, this is not a statement because square of 3 is 9 which is odd and square of  4 is 16 which is even. so it can be both true and false.  

(v) The sides of a quadrilateral have equal length.

Solution:

No , this is not a statement because square is a quadrilateral which has all sides equal but for rectangle which is also a quadrilateral in which all sides are not equal. so it can be both true and false.  

(vi) Answer this question.

Solution:

No, this is not a statement because this an order and we cannot say whether it is true or false.

(vii) The product of (–1) and 8 is 8.

Solution:

Yes , this is a statement because product of -1 and 8 is -8 and therefore this is definitely  false.  

(viii) The sum of all interior angles of a triangle is 180°.

Solution:

Yes, this is a statement because sum of all interior triangle is  180° in a triangle and  therefore this is definitely  true.

(ix) Today is a windy day.

Solution:

No, this is not a statement because a day can be either windy or not windy we cannot say whether it is true or false.

(x) All real numbers are complex numbers.

Solution:

Yes , this is a statement because all real numbers are complex with imaginary part as 0 and  therefore this is definitely  true.

Question 2. Give three examples of sentences which are not statements. Give reasons for the answers?

Solution:

1. How far is Chennai from here? This is a question which also contains the word “Here”. Hence it is not a statement
2. Tomorrow is Friday. This sentence can either be true or false hence it is not a statement.
3. The sum of x and y is greater than 0 .Here, we are not in a position to determine whether it is true or false, unless we know what x and y are and therefore this is not a statement.

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