## NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Exercise 14.1

Here you will find the NCERT Solutions of Chapter 14 Mathematical Reasoning Exercise 14.1 will help you in finding solutions of difficult questions. Class 11 Maths NCERT Solutions provided here are prepared by subject matter experts of Studyrankers. It will help you in improving your marks in the examinations and knowing the basic concepts of the chapter.

1. 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 180Âº.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

**Answer**

(i) The given sentence is always false because the maximum number of days in a month is 31. Therefore, it is a statement.

(ii) The given sentence is not a statement because for some people Mathematics can be easy and for some other, it can be difficult.

(iii) Statement: It true that the sum of 5 and 7 is greater than 10.

(iv) Sentence: The square of a number may be even or it may be odd. e.g. 22 = 4 (even), 32 = 9 (odd). (v) Sentence: A quadrilateral may have equal lengths as it may be a rhombus or a square or the quadrilateral may have unequal sides.

(vi) Sentence: It is an order.

(vii) Statement: It is false because product of (–1) and 8 is not 8.

(viii) This sentence is always true and therefore, it is a statement.

(ix) Sentence: It is a windy day which day it is?

(x) Statement: It is true that all real numbers are complex number of the form a + i.

2. Give three example of sentences which are not statements. Give reasons for the answers.

**Answer**

(i) It is a rainy month. We can not say which month is rainy.

(ii) She is very beautiful. Who is beautiful?

(iii) You are a brave boy. Who is brave?