Mathematical Reasoning

A mathematical sentence is a sentence that states a fact or contains a complete idea. A sentence that can be judged to be true or false is called a statement or a closed sentence. The negation of a statement is a statement with the opposite meaning. It is usually constructed by adding a 'not' or removing a 'not' from the statement. Some of the connecting words which are found in compound statements like 'And', 'Or’ are often used in mathematical statements. These are called connectives. Quantifiers are the words that are used to indicate the number of objects or cases in a statement. 'There exists' and 'For every' are the two phrases known as quantifiers. The statements of the form 'if p then q', 'p only if q' and 'if and only if' are called implications. Given an if-then statement 'if p, then q', we can create other related statements: To form the converse of the conditional statement, interchange the antecedent and the consequent. Here, we have learned, how to check the validity of a statement, i.e., how to check when it is true and when it is not true. The truth and falsity of the statement depends upon the following: Special words: 'and', 'or' Implications: 'if-then', 'if and only if' Quantifiers: 'for every', 'there exists'.

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