Read Chapter 14 Mathematical Reasoning of NCERT Class 11 Mathematics
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Chapter 14 Mathematical Reasoning PDF Resource
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14.1 Overview
If an object is either black or white, and if it is not black, then logic leads us to the conclusion that it must be white. Observe that logical reasoning from the given hypotheses can not reveal what “black” or “white” mean, or why an object can not be both. Infact, logic is the study of general patterns of reasoning, without reference to particular meaning or context.
14.1.1 Statements
A statement is a sentence which is either true or false, but not both simultaneously. Note: No sentence can be called a statement if
(i) It is an exclamation
(ii) It is an order or request
(iii) It is a question
(iv) It involves variable time such as ‘today’, ‘tomorrow’, ‘yesterday’ etc.
(v) It involves variable places such as ‘here’, ‘there’, ‘everywhere’ etc.
(vi) It involves pronouns such as ‘she’, ‘he’, ‘they’ etc.
Example 1
(i) The sentence ‘New Delhi is in India; is true. So it is a statement.
(ii) The sentence “Every rectangle is a square” is false. So it is a statement.
(iii) The sentence “Close the door” can not be assigned true or false (Infact, it is a command). So it can not be called a statement.
(iv) The sentence Chapter 14 MATHEMATICAL REASONING
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