# NCERT Class 11 Maths Mathematical Reasoning

## Chapter 14 Ex.14.1 Question 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.

(vii) The product of $$\left( -1 \right)$$ and $$8$$ is $$8.$$

(viii) The sum of all interior angles of a triangle is $$180^\circ .$$

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

### Solution

(i) This sentence is incorrect because the maximum number of days in a month is $$31.$$ Hence, it is a statement.

(ii) This sentence is subjective in the sense that for some people mathematics can be easy and for some others it can be difficult. Hence, it is not a statement.

(iii) The sum of $$5$$ and $$7$$ is$$12,$$ which is greater than $$10.$$Therefore, this sentence is always correct. Hence, it is a statement.

(iv) This sentence is sometimes correct and sometimes incorrect. For example, the square of $$2$$ is an even number. However, the square of $$3$$ is an odd number. Hence, it is not a statement.

(v) This sentence is sometimes correct and sometimes incorrect. For example, squares and rhombus have sides of equal lengths. However, trapezium and rectangles have sides of unequal lengths. Hence, it is not a statement.

(vi) It is an order. Therefore, it is not a statement.

(vii) The product of $$\left( -1 \right)$$ and $$8$$ is $$\left( -8 \right).$$ Therefore, the given sentence is incorrect. Hence, it is a statement.

(viii) This sentence is correct and hence, it is a statement.

(ix) The day that is being referred to is not evident from the sentence. Hence, it is not a statement.

(x) All real numbers can be written as $$a + i \times 0.$$ Therefore, the given sentence is always correct. Hence, it is a statement.

## Chapter 14 Ex.14.1 Question 2

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

### Solution

The three examples of sentences, which are not statements, are as follows.

(i) $${a^2}$$ is always greater than $$1.$$

Unless, we know what $$a$$ is, we cannot say whether the sentence is true or not. Therefore, it is not a statement

(ii) He is an engineer.

It is not evident from the sentence as to whom ‘he’ is referred to. Therefore, it is not a statement

(iii) Mathematics is Easy.

This is not a statement because for some people, Mathematics may be difficult and for some others, it may be difficult. Therefore, it is not a statement.