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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.
Chapter 14 Mathematical Reasoning
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.
Download pdf of NCERT Solutions for Class Mathematics Chapter 14 Mathematical Reasoning
Exercise 1
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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If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
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A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
- Q:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
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The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
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How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
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Find the sum of all numbers between 200 and 400 which are divisible by 7.
- Q:- Write the following sets in roster form:
(i) A = {x: x is an integer and - 3 < x < 7}.
(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.
Recently Viewed Questions of Class 11 Mathematics
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For what values of x, the numbers
are in G.P? - Q:-
The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.
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Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and classified as defective (D) or non-defective (N). Write the sample space of this experiment?
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If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.
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Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.
Prove that
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The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
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A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?
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If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are
. - Q:-
The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.
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How many 5–digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?
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