**CBSE NCERT Solutions For Class 11 Maths Chapter 14: **This NCERT Class 11 Maths Chapter 14 discusses some basic ideas of Mathematical Reasoning. Everyone knows that human beings evolved from the lower species over many millennia. The main asset that made humans ‘superior’ to other species was the ability to reason. In mathematical language, there are two kinds of reasoning- inductive and deductive. Inductive reasoning has already been discussed with you in the context of mathematical induction. This NCERT Class 11 Maths Chapter 14 will be discussing some fundamentals of deductive reasoning.

By solving the NCERT Solutions For Class 11 Maths Chapter 14, you 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. Whenever we mention a statement here, it is a ‘mathematically acceptable’ statement. Solving the Solutions for NCERT Class 11 Maths Chapter 14 will further aid in clearing any confusion students might face on this topic. We get you completely solved NCERT Solutions for Class 11 Maths Chapter 14 by the top teachers at Embibe.

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

The topics and sub-topics of NCERT Class 11 Maths Chapter 14 Mathematical Reasoning will assist you in your CBSE Class 11 Maths Preparation. The topics and sub-topics of this topic will aid you in preparing well for the CBSE Exam. This will also help you in understanding the topics under NCERT Class 11 Maths Chapter 14:

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. Download and solve the Solutions for NCERT Class 11 Maths Chapter 14 PDF given below.

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

We can also look into 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.

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This article on CBSE NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning will be helpful to you in clearing your doubts regarding this topic. You should also solve the NCERT Solutions for Class 11 Maths Chapter 14 PDF to have the best preparation ahead. Also, solve previous year papers and take a sufficient amount of mock tests. Taking free **JEE Main Mock Test** on Embibe will help you if you further aim to take competitive exams. The tests on Embibe are specially formulated to help you gain confidence and work on your time-management skill.

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