Ppt 9th state poofs in introduction
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This document discusses proofs in mathematics and statements. It defines a statement as an assertion that can be determined to be true or false, with a truth value of either T (true) or F (false). Examples of clear true and false statements are provided. It notes that some statements are conditionally true or false, depending on additional information. A statement must be unambiguous and cannot refer to itself or use ambiguous language to be considered a statement for the purposes of proofs.
Ppt 9th state poofs in introduction
- 2. PROOFS IN MATHEMATICS Get Started STATEMENTS www.teachlearnweb.com MIND MAP
- 3. We come across many statements in our daily life. We gauge the worth of each statement. Some statements we consider to be appropriate and true and some we dismiss. There are some we are not sure of. How do we make these judgments? GET STARTED
- 4. The sentences that can be judged on some criteria, no matter by what process for their being true or false are statements. A statement is an assertion that can be determined to be true or false. The truth value of a statement is T if it is true and F if it is false. . www.teachlearnweb.com STATEMENT
- 5. www.teachlearnweb.com Look at the following sentences which of them are clearly false or clearly true. These are statements. We say these sentences that can be judged on some criteria, no matter by what process for their being true or false are statements. Examples: 1. New York is the capital of USA (F) 2. 3 + 2 = 5 (T) 3. The sun rises in the east. 4. 3 + 2 = 5 5. 4 > 8 Besides those there are some other sentences that are true for some known cases but not true for other cases, for example x + 2 = 7 is true only when x = 5 and x < y is only true for those values of x and y where x is less than y. A statement that is always true is called logically true or a tautology. A statement that is always false is called logically false or a contradiction EXAMPLES
- 6. www.teachlearnweb.com NOT A STATEMENT • All these the sentences are not statements. • Only those that can be judged to be true or false but not both are statements. A statement can not be ambiguous. The sentences which are talking about Themselves and the sentences with possibility are not statements .
- 7. Look at the sentence: “You may find water on the moon “(ambiguity) It is not a statement because this sentence have words that show only likely or possibility and hence ambiguity of being on both sides. 1. Please ignore this notice..... 2. The statement I am making is false. 3. This sentence has some words. www.teachlearnweb.com EXAMPLES
- 8. Look at the sentences like “Humans are meant to rule the earth” “Ramu is a good driver.” These sentences are ambiguous sentences as the meaning of ruling the earth is not specific. Similarly, the definition of a good driver is not specified. Consider some of the other sentences like “The earth has one Moon” “Bhaskara has written the book "Leelavathi“” Think about how would you verify these to consider as statements? These are not ambiguous statements but needs to be tested. They require some observations or evidences. Besides, checking this statement cannot be based on using previously known results. The first sentence require observations of the solar system and more closely of the earth. The second sentence require other documents, references or some other records. www.teachlearnweb.com EXAMPLES