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Q1 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.
Ans: (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 (–1) and 8 is (–8). 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 × 1 + 0 × i. Therefore, the given sentence is always correct. Hence, it is a statement.
Q2 Give three examples of sentences which are not statements. Give reasons for the answers.
Ans: The three examples of sentences, which are not statements, are as follows.
(i) He is a doctor.
It is not evident from the sentence as to whom ‘he’ is referred to. Therefore, it is not a statement.
(ii) Geometry is difficult.
This is not a statement because for some people, geometry can be easy and for some others, it can be difficult.
(iii) Where is she going?
This is a question, which also contains ‘she’, and it is not evident as to who ‘she’ is. Hence, it is not a statement.
Mathematical Reasoning Question Answers: NCERT Class 11 Mathematics
Welcome to the Chapter 14 - Mathematical Reasoning, Class 11 Mathematics - NCERT Solutions page. Here, we provide detailed question answers for Chapter 14 - Mathematical Reasoning.The page is designed to help students gain a thorough understanding of the concepts related to natural resources, their classification, and sustainable development.
Our solutions explain each answer in a simple and comprehensive way, making it easier for students to grasp key topics and excel in their exams. By going through these Mathematical Reasoning question answers, you can strengthen your foundation and improve your performance in Class 11 Mathematics. Whether you're revising or preparing for tests, this chapter-wise guide will serve as an invaluable resource.
If we consider mathematics, there are mainly two types of reasoning - 1) Inductive reasoning, 2.) Deductive reasoning. Inductive reasoning is studied in principle of mathematical induction. Deductive reasoning will be discussed in this chapter. Examples or situations in this chapter mostly related to real life and some with mathematics. This chapter consists of mathematically acceptable statements, connecting words/phrases - "it and only if", "implies”, "and/or", "implied by", "there exists” and their use through variety of examples related to real life and mathematics, difference between contradiction, converse and contrapositive.
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Exercise 1
Key Features of NCERT Class 11 Mathematics Chapter 'Mathematical Reasoning' question answers :
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Popular Questions of Class 11 Mathematics
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Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
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(ii) B = {x: x is a natural number less than 6}.
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}
(iv) D = {x: x is a prime number which is divisor of 60}.
(v) E = The set of all letters in the word TRIGONOMETRY.
(vi) F = The set of all letters in the word BETTER. - Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
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Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
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