<\/span><\/h2>\nThe different sections in Chapter 14 of CBSE Maths Class 11 must be solved thoroughly before the exam starts. Additionally, students must revisit old topics and revise regularly. Students can go through the Class 11 Maths solutions chapter 14 pdf download on our website.\u00a0<\/p>\n
While studying the Class 11 Maths Chapter 14 Mathematical Reasoning, you may come across sentences like \u2018One plus one equals two\u2019\u2019. <\/em>\u201cAll prime numbers are odd numbers<\/em>\u201c. Of these sentences, the first one is true and the second one is false. When there is no ambiguity regarding the sentences they are statements.<\/p>\nThink of a sentence that is vague or ambiguous? Consider the sentence: \u2018The sum of a and b is greater than 0.\u2019 Here, we are not in a position to determine whether it is true or false unless we know what a and b are. For example, it is false where a=1, b= -5 and true when x=1 and y=0. Therefore, this sentence is not a statement. But the sentence: For any natural numbers a and b, the sum of a and b is greater than 0 is a statement.<\/p>\n
In Short, mathematical reasoning is a sentence that is either true or false. It may contain words and symbols. Another example – \u201cThe square root of 4 is 5\u201d is a mathematical statement (which is, of course, not true).<\/p>\n
Class 11 Maths Chapter 14 Mathematical Reasoning Mathematical Reasoning has 5 exercises. There is a total of 13 topics including the introduction. The sections of chapter 14 are given as follows:<\/p>\n
\n- 14.1 Introduction<\/li>\n
- 14.2 Statements<\/li>\n
- 14.3 New Statements from Old<\/li>\n
- 14.3.1 Negotiation of a Statement<\/li>\n
- 14.3.2 Compound Statements<\/li>\n
- 14.4 Special Words\/ Phrases<\/li>\n
- 14.4.1 The word \u201cAnd\u201d<\/li>\n
- 14.4.2 The word \u2018or\u2019<\/li>\n
- 14.4.3 Quantifiers<\/li>\n
- 14.5 Implications<\/li>\n
- 14.5.1 Contrapositive and Converse<\/li>\n
- 14.6 Validating Statements<\/li>\n
- 14.6. By Contradiction<\/li>\n<\/ul>\n
We can also look into a method for producing new statements from those that we already have. Study of statements, let\u2019s take a look at an important technique that we may use 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.<\/p>\n
Secondly, CBSE Class 11 Maths Chapter 14 Mathematical Reasoning – 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 \u2018and\u2019, \u2018or\u2019, etc.<\/p>\n