**CBSE NCERT Solutions For Class 11 Maths Chapter 14 PDF Download: **The solutions provided in this article will cover all the 5 exercises given in the chapter. The Mathematical Reasoning chapter solutions are prepared by industry experts at Embibe with years of teaching experience in Maths. The solutions will help students to understand the logic behind solving the questions.

The mathematics chapter 14 class 11 solutions will aid students in completing their homework on time. By solving the NCERT exercise questions students will get knowledge about the theorems in the chapter, they will know that the basic unit involved in mathematical reasoning is a mathematical statement. A sentence is called a mathematically acceptable statement if it is either true or false but not both. Each exercise focus on one or the other aspect of Mathematical Reasoning. Learners will be able to download the pdf through the link given below in this article:

## NCERT Solutions For Class 11 Maths Chapter 14: Mathematical Reasoning

NCERT Class 11 Maths Chapter 14 Mathematical Reasoning has 5 exercises. There is a total of 13 topics including the introduction.

14.1 | Introduction |

14.2 | Statements |

14.3 | New Statements from Old |

14.3.1 | Negation of a Statement |

14.3.2 | Compound Statements |

14.4 | Special Words/Phrases |

14.4.1 | The word “And” |

14.4.2 | The word “Or” |

14.4.3 | Quantifiers |

14.5 | Implications |

14.5.1 | Contrapositive and Converse |

14.6 | Validating Statements |

14.6.1 | By Contradiction |

### NCERT Solutions For Class 11 Maths Chapter 14 PDF Download

While studying the NCERT Class 11 Maths Chapter 14, you may come across sentences like ‘*Two plus two equals four*“. “*The sum of two positive numbers is positive*“. “*All prime numbers are odd numbers*“. Of these sentences, the first two are true and the third one is false. There is no ambiguity regarding these sentences. Therefore, they are statements.

Can you think of an example of a sentence which is vague or ambiguous? Consider the sentence: ‘The sum of x and y is greater than 0.’ Here, we are not in a position to determine whether it is true or false unless we know what x and y are. For example, it is false where x=1, y= -3 and true when x=1 and y=0. Therefore, this sentence is not a statement. But the sentence: For any natural numbers x and y, the sum of x and y is greater than 0 is a statement. Now that you know what you will be studying in this chapter we have attached the images for the pdf you can download through the link given after the images.

### NCERT Solutions For Class 11 Maths Chapter 2 Important Questions

Below are some of the important questions that can be asked in the exams.

Short answer type questions1. Write the range of a Signum function.2. The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0,1). Find the set A and the remaining elements of A × A. 3. Express the function f: A—R.f(x) = x^{2} – 1. where A = { -4, 0, 1, 4) as a set of ordered pairs. |

Long answer type questions1. Find the domain and range of the real function f(x) = x/1+x^{2}. 2. Draw the graph of the function f: R → R defined by f (x) = x^{3}, x∈R 3. If R_{3} = {(x, x ) | x is a real number} is a relation, then find the domain and range of R_{3}. |

### NCERT Solutions For Class 11 Maths Chapter 14: Mathematical Reasoning

We can also look into a method for producing new statements from those that we already have. An English mathematician, ‘George Boole’ discussed these methods in his book ‘The Laws of Thought’ in 1854. Here, we can see two techniques. As the first step in the study of statements, we look at an important technique that we may use in order to deepen the understanding of mathematical statements. This technique is to ask not only what it means to say that a given statement is true but also what it would mean to say that the given statement is not true. CBSE NCERT Class 11 Maths Chapter 14 Mathematical Reasoning also tells that the denial of a statement is called the negation of the statement. Many mathematical statements are obtained by combining one or more statements using some connecting words like ‘and’, ‘or’, etc.

### Important Information on Mathematical Reasoning Class 11 Maths

Below are the 5 important points on Chapter 14 Class 11 Maths:

- A statement is a sentence when it is mathematically accepted. It can be either false or true.
- What is the negation of a statement: Take a statement and denote it by s then its negation will be denoted by ~s.
- There are 4 methods that can be used to check the validity of a statement. (1) Direct Method (2) Contrapositive Method (3) Method of Contradiction (iv) By using a Counterexample.
- We can use “If ”, “only if ”, “ if and only if ” as implications in a statement.
- Compound Statement: When a statement is made up of 2 or more smaller parts (component statements) it is known as a compound statement.

### Preparations Tips for Class 11 Chapter 2

We know that after having the solutions students might still face difficulties in solving questions. What you can do is solve the questions one by one without leaving any questions. First, study the topics and then start solving the questions. Take proper breaks while solving and if you face any difficulty then only look for the solutions. You can lear the chapter as well as take the test to improve your study pattern.

Study Mathematical Modelling Here For Free |

NCERT Solutions for Class 11 Maths Chapter 13 | NCERT Solutions for Class 11 Maths Chapter 15 | NCERT Solutions for Class 11 Maths (All Chapter) |

If you are looking for other exercise solutions also you can check the above links. While if you wish to improve your score and perform better you can take the free mock test by Embibe.

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