Mathematical Reasoning – Exercise 14.1 – Class XI

  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 180°.

(ix) Today is a windy day.

(x) All real numbers are complex numbers

Solution:

(i) since the maximum number of days in a month is 31, therefore the given statement is incorrect. Thus it is a statement.

(ii) This sentence is subjective because it depends on mindset of the people, for some people mathematics can be easy and for some others, it can be difficult. Hence, it is not a statement.

(iii) The given sentence is always correct since the sum of 5 and 7 is 12, which is greater than 10. Therefore, 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 and also the square of 5 is 25 which 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) The sentence ‘answer this question’ is an order. Therefore, it is not a statement.

(vii) The given sentence is incorrect because we know that the product of (–1) and 8 is (–8). Hence, it is a statement.

(viii )Yes sum of all the three interior angles is 180 degrees. The given sentence is correct and hence, it is a statement.

(ix) The given sentence ‘today is a windy day’ doesn’t specifies any particular date so it is not a statement.

(x) All real numbers can be written as a × 1 + 0 × i. Therefore, the given sentence is always correct. Hence, it is a statement.


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

Solution:

(i)I have exam on tomorrow.

It is not evident from the sentence as date is not mentioned. Therefore, it is not a statement.

(i) Science is tricky.

The sentence ‘science is tricky’ is not same for all. For some people science might be easy and for some it might be difficult. So the sentence is not a statement.

(iii) He is an engineer.

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