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Class XI Chapter 14 – Mathematical Reasoning Maths ______________________________________________________________________________ Question 2: Give three examples of sentences which are not statements. Give reasons for the answers. Solution 2: 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. Exercise 14.2 Question 1: Write the negation of the following statements: (i) Chennai is the capital of Tamil Nadu. (ii) 2 is not a complex number. (iii) All triangles are not equilateral triangle. (iv) The number 2 is greater than 7. (v) Every natural number is an integer. Solution 1: (i) Chennai is not the capital of Tamil Nadu. (ii) 2 is a complex number. (iii) All triangles are equilateral triangles. (iv) The number 2 is not greater than 7. (v) Every natural number is not an integer. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.
Class XI Chapter 14 – Mathematical Reasoning Maths ______________________________________________________________________________ Question 2: Are the following pairs of statements negations of each other? (i) The number x is not a rational number. The number x is not an irrational number. (ii)The number x is a rational number. The number x is an irrational number. Solution 2: (i) The negation of the first statement is â€œ the number x is a rational number â€. This is same as the second statement. This is because if a number is not an irrational number, then it is a rational number. Therefore, the given statements are negations of each other. (ii) The negation of the first statement is â€œ the number x is not a rational number â€. This means that the number x is an irrational number, which is the same as the second statement. Therefore, the given statements are negations of each other. Question 3: Find the component statements of the following compound statements and check whether they are true or false. (i) Number 3 is prime or it is odd. (ii) All integers are positive or negative. (iii) 100 is divisible by 3, <strong>11</strong> and 5. Solution 3: (i) The component statements are as follows. p: Number 3 is prime. q: Number 3 is odd. Both the statements are true. (ii) The component statements are as follows. p: All integers are positive. q: All integers are negative. Both the statements are false. (iii) The component statements are as follows. p: 100 is divisible by 3. q: 100 is divisible by <strong>11</strong>. r: 100 is divisible by 5. Here, the statements, p and q, are false and statement r is true. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.
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Class XI Chapter 1 - Sets Maths ___
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Class XI Chapter 2 - Relations and
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Class XI Chapter 3 - Trigonometric
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Class XI Chapter 4 - Principle of M
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Class XI Chapter 5 - Complex Number
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Class XI Chapter 6 - Linear Inequal
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Class XI Chapter 7 - Permutation an
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Class XI Chapter 8 - Binomial Theor
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Class XI Chapter 9 - Sequences and
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Class XI Chapter 10 - Straight Line
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Class XI Chapter 11 - Conic Section
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Class XI Chapter 12 - Introduction
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Class XI Chapter 13 - Limits and De
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Page 491: Class XI Chapter 14 - Mathematical
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Page 507 and 508: Class XI Chapter 15 - Statistics Ma
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