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Mathematical Logic and Counterexamples Exploration

Delve into the concept of counterexamples in mathematics, from disproving statements to exploring complex proofs. Work on practice problems involving inequalities and negatives. Homework on Page 18 in the packet, Section 1.1: 32-34, 50-56.

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Mathematical Logic and Counterexamples Exploration

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  1. Section 1.1 Part III English to Math and Counterexamples

  2. Examples: Rewrite the English statement into a mathematical statement. • x is more than y. • x is five more than y. • the number c is negative. • eight less than the product of y is nine. • x is a least two.

  3. In mathematics, proving a statement is true can often involve rather complicated proofs. Proving that a statement is false is a much easier task. To prove that a statement is false, you must ____________________________, called a _______________. give 1 false statement counterexample

  4. Examples: Show a counter example for each statement. • All prime numbers are odd. • 2. The square root of a number is always less than or equal to the number. • 3. have to take the square root of a number less than 1 This counterexample disproves this property

  5. Your homework is……………………… Page 18 in the homework packet Section 1.1: 32-34, 50-56

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