NCERT Solutions for Class 11 Maths Chapter 14: Mathematical Reasoning - Exercise 14.1

Exercise 14.1

Refer to page 3 for Exercise 14.1 in the PDF.

1. Which of the following sentences are statements? Give reasons for your answer.

i. There are 35 days in a month.

Ans: A mathematical statement is that sentence which can be classified as either true or false.  

The given sentence is that there are 35 days in a month. This sentence is not correct. This is because the maximum number of days in a month can be 31. 

Hence, the given sentence is false.

Therefore, the given sentence is a statement.

ii. Mathematics is difficult.

Ans: A mathematical statement is that sentence which can be classified as either true or false.  

The given sentence is that mathematics is difficult. This sentence is neither correct nor false. This is because it varies or changes from person to person. Some people can find mathematics to be difficult while others can find it easy. So, this statement is subjective. 

Hence, the given sentence is neither true nor false.

Therefore, the given sentence is not a statement.

iii. The sum of 5 and 7 is greater than 10.

Ans: A mathematical statement is that sentence which can be classified as either true or false.  

The given sentence is that the sum of 5 and 7 is greater than 10. This sentence is correct. This is because the sum of 5 and 7 is 12. And we know that 12 is greater than 10. So, the sum of 5 and 7 is greater than 10. So, this sentence is correct.

Hence, the given sentence is true.

Therefore, the given sentence is a statement.

iv. The square of a number is an even number.

Ans: A mathematical statement is that sentence which can be classified as either true or false.  

The given sentence is that the square of a number is an even number. This sentence is not completely correct.

Consider the number 2. The square of 2 is 4, which is an even number.

Similarly, consider the number 3. The square of 3 is 9, which is an odd number. 

So, the given statement can be correct and incorrect both as the square of a number can be both even and odd. 

Hence, the given sentence is neither true nor false.

Therefore, the given sentence is not a statement.

v. The sides of a quadrilateral have equal length.

Ans: A mathematical statement is that sentence which can be classified as either true or false.  

The given sentence is that the sides of a quadrilateral have equal length. This sentence is not completely correct.

A quadrilateral is a four-sided closed and convex polygon. 

Consider the quadrilaterals like parallelograms, rectangles, kites, and trapeziums. All these quadrilaterals have unequal lengths of sides.

Similarly, consider the quadrilaterals like rhombuses and squares. These quadrilaterals have equal lengths of sides. 

So, the given statement can be correct and incorrect both as the sides of a quadrilateral can be both equal and unequal. 

Hence, the given sentence is neither true nor false.

Therefore, the given sentence is not a statement.

vi. Answer this question.

Ans: A mathematical statement is that sentence which can be classified as either true or false.  

The given sentence is that answer this question. This is an imperative sentence. 

Imperative sentences are those that are used to issue commands or orders. In order words, imperative sentences are commands or orders.

Hence, the given sentence is an order. 

Therefore, the given sentence is not a statement.

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

Ans: A mathematical statement is that sentence which can be classified as either true or false.  

The given sentence is that the product of $\left( { - 1} \right)$ and 8 is 8. This sentence is not correct. This is because the product of $\left( { - 1} \right)$ and 8 is not 8. 

$\left( { - 1} \right) \cdot 8 \ne 8$

And we know that the product of $\left( { - 1} \right)$ and 8 is $\left( { - 8} \right)$. 

$\left( { - 1} \right) \cdot 8 = \left( { - 8} \right)$

So, this sentence is not correct.

Hence, the given sentence is false.

Therefore, the given sentence is a statement.

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

Ans: A mathematical statement is that sentence which can be classified as either true or false.  

The given sentence is that the sum of all the interior angles of a triangle is $180^\circ $. This sentence is correct. This is because according to the ‘sum of the interior angles of a triangle’ theorem, the sum of all the interior angles of a triangle is $180^\circ $.

Hence, the given sentence is true.

Therefore, the given sentence is a statement.

ix. Today is a windy day.

Ans: A mathematical statement is that sentence which can be classified as either true or false.  

The given sentence is that today is a windy day. This sentence is neither correct nor false. This is because the day being referred to in the statement is ambiguous. The day is not evident from the given sentence. So, this statement is subjective. 

Hence, the given sentence is neither true nor false.

Therefore, the given sentence is not a statement.

x. All real numbers are complex numbers.

Ans: A mathematical statement is that sentence which can be classified as either true or false.  

The given sentence is that all real numbers are complex numbers. This sentence is correct. This is because all real numbers can be expressed in the form of a complex number in the following manner.

Let $a\in R$

$a$ can be written as $a+0i$ where a is the real part and 0 is the imaginary part.

Hence $a\in C$

Hence, the given sentence is true.

Therefore, the given sentence is a statement.

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

Ans: A mathematical statement is that sentence which can be classified as either true or false.  

The three examples of such sentences that are not mathematical statements are as follows –

1. Ajay plays the musical instrument. 

From the given statement it is not clear that Ajay plays which musical instrument. Hence, it cannot be determined whether the given sentence is true or false. Therefore, the given sentence, ‘Ajay plays the musical instrument’, is not a statement.

2. Physics is a difficult subject. 

From the given sentence it cannot be determined whether Physics is a tough subject or not. This is because it varies and changes from person to person. Some people can find physics to be difficult while others can find it easy. So, this statement is subjective. Hence, the given sentence is neither true nor false. Therefore, the given sentence, ‘Physics is a difficult subject’, is not a statement. 

3. What is he doing?

The given sentence makes it clear that it is an interrogative sentence. This is because a question is being asked in the given sentence. Therefore, the given sentence, ‘What is he doing?’, is not a statement.

NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Exercise 14.1

Opting for the NCERT solutions for Ex 14.1 Class 11 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 14.1 Class 11 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 11 students who are thorough with all the concepts from the Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 11 Maths Chapter 14 Exercise 14.1 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

Besides these NCERT solutions for Class 11 Maths Chapter 14 Exercise 14.1, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it. 

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