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NCERT Solutions for Exercise 14.1 Class 11 Maths Chapter 14 - Mathematical Reasoning
Edited By Safeer PP | Updated on Jul 13, 2022 05:33 PM IST
In mathematics, there are two kinds of reasoning. Inductive reasoning and deductive reasoning. The NCERT Class 11 Maths chapter 4 has mathematical reasoning have introduced a method of inductive reasoning. Chapter 14 of Class 11 Maths gives the fundamentals of deductive reasoning.
Exercise 14.1 Class 11 Maths gives questions to check whether the given sentence is a statement or not. Class 11 Maths chapter 14 exercise 14.1 moves around the concepts of statement and students can access NCERT Solutions for Class 11 Maths chapter 14 exercise 14.1 for free on this page. The chapter mathematical reasoning of NCERT books have the following exercises other than Class 11th Maths chapter 14 exercise 14.1
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- Mathematical Reasoning Exercise 14.2
- Mathematical Reasoning Exercise 14.3
- Mathematical Reasoning Exercise 14.4
- Mathematical Reasoning Exercise 14.5
- Mathematical Reasoning Miscellaneous Exercise
Mathematical Reasoning Class 11 Chapter 14 Exercise 14.1
Question:1.(i) Which of the following sentences are statements? Give reasons for your answer.
There are 35 days in a month.
Answer:
There are 30 or 31 days in a month (And 28 or 29 in some cases). The given sentence is false. Hence it is a statement.
Question:1.(ii) Which of the following sentences are statements? Give reasons for your answer.
Mathematics is difficult.
Answer:
Mathematics can be difficult for some and easy for others. So it is neither true nor false. Hence it is not a statement.
Question:1.(iii) Which of the following sentences are statements? Give reasons for your answer.
The sum of 5 and 7 is greater than 10.
Answer:
Sum of 5 and 7 = 5 + 7 = 12 > 10. Hence the sentence is true. So it is a statement.
Question:1.(iv) Which of the following sentences are statements? Give reasons for your answer.
The square of a number is an even number.
Answer:
, which is even, and
, which is odd. So the square of a number may be even or may be odd. Hence it is not a statement.
Question:1.(v) Which of the following sentences are statements? Give reasons for your answer.
The sides of a quadrilateral have equal length.
Answer:
The sentence is true for square and rhombus but not true for the rectangle. Hence it is not a statement.
Question:1.(vi) Which of the following sentences are statements? Give reasons for your answer.
Answer this question.
Answer:
The give sentence is an order. Hence it is not a statement.
Question:1.(vii) Which of the following sentences are statements? Give reasons for your answer.
The product of (–1) and 8 is 8.
Answer:
The product of (-1) and 8 = -1 x 8 = -8. Hence the given sentence is false. So it is a statement.
Question:1.(viii) Which of the following sentences are statements? Give reasons for your answer.
The sum of all interior angles of a triangle is 180 °.
Answer:
The sum of all interior angles of a triangle is 180 °. This sentence is true always. Hence this is a statement.
Question:1.(ix) Which of the following sentences are statements? Give reasons for your answer.
Today is a windy day.
Answer:
This may be true or false. Hence this is not a statement.
Question:1.(x) Which of the following sentences are statements? Give reasons for your answer.
All real numbers are complex numbers.
Answer:
All real numbers can be written in the form of a + i(0) (when a is a real number). This shows that all real numbers are complex numbers. Hence the sentence is always true. So it is a statement.
Question:2 Give three examples of sentences which are not statements. Give reasons for the answers.
Answer:
Following are three examples of sentences which are not statements.
How beautiful!
- This is an exclamation. Hence not a statement.
Open the door.
- This is an order. Hence not a statement.
Where are you going?
- This is a question. Hence not a statement.
More About NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2
There are eleven questions including the sub-questions in exercise 14.1 Class 11 Maths. First 10 questions of Class 11 Maths chapter 14 exercise 14.1 is to check whether the given sentence is a statement or not. And the main question number 2 of Class 11 Maths chapter 14 exercise 14.1 is to give some sentences that are not statements. A few examples are also given in the NCERT Class 11 Maths book prior to the Class 11th Maths chapter 14 exercise 14.1
Also Read| Mathematical Reasoning Class 11 Notes
Benefits of NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.1
Solving the exercise 14.1 Class 11 Maths give exposure to the definition of a mathematical statement.
A general purpose of solving the NCERT exercises is to get a strong idea of concepts and the NCERT solutions for Class 11 Maths chapter 14 exercise 14.1 helps for the same.
Also see-
NCERT Solutions of Class 11 Subject Wise
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Frequently Asked Questions (FAQs)
1. What is a statement in mathematics?
In mathematics, a sentence is called a statement when it is either true or false
2. Give two statements
There are 60 days in a year
The sum of 10 and 5 is greater than 10
3. Give examples of sentences that are not a statement
Physics is difficult
Eating is fun
4. The 1st treatise on logic was written by………..?
Aristotle
5. Founder of the modern subject of symbolic logic?
Augustus De Morgan
6. What number of questions are solved in exercise 14.1 Class 11 Maths?
11 questions including sub-questions are explained in the NCERT solutions for Class 11 Maths chapter 14 exercise 14.1
7. How many exercises are given in the chapter mathematical reasoning?
6 exercises
8. Which NCERT Class 11 Maths chapter covers the concept of induction?
Chapter 4 Mathematical Reasoning.
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