Statements Bernd Schr oder logo1 Bernd Schr oder Louisiana Tech - PowerPoint PPT Presentation

Definition Examples Truth Values Statements Bernd Schr¨ oder logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values A statement or proposition is a sentence that is either true or false. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values A statement or proposition is a sentence that is either true or false. 1. Any mathematical result is a statement. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values A statement or proposition is a sentence that is either true or false. 1. Any mathematical result is a statement. 2. Ideally, so is every sentence in a proof logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values A statement or proposition is a sentence that is either true or false. 1. Any mathematical result is a statement. 2. Ideally, so is every sentence in a proof, but prose can be used to explain and loosen up the structure. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values A statement or proposition is a sentence that is either true or false. 1. Any mathematical result is a statement. 2. Ideally, so is every sentence in a proof, but prose can be used to explain and loosen up the structure. 3. We need not know whether a statement is true or false to identify it as a statement. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Following is a Statement? logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Following is a Statement? 1. The number 97 is prime. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Following is a Statement? 1. The number 97 is prime. (Statement.) logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Following is a Statement? 1. The number 97 is prime. (Statement.) 2. The number 97 is a twin prime. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Following is a Statement? 1. The number 97 is prime. (Statement.) 2. The number 97 is a twin prime. (Statement.) logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Following is a Statement? 1. The number 97 is prime. (Statement.) 2. The number 97 is a twin prime. (Statement.) 3. Which of the following is a statement? logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Following is a Statement? 1. The number 97 is prime. (Statement.) 2. The number 97 is a twin prime. (Statement.) 3. Which of the following is a statement? (Not a statement.) logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Following is a Statement? 1. The number 97 is prime. (Statement.) 2. The number 97 is a twin prime. (Statement.) 3. Which of the following is a statement? (Not a statement.) ∞ 1 ∑ 4. All zeros of the Riemann Zeta function ζ ( z ) = n z lie n = 1 on the straight line ℜ ( z ) = 1 2. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Following is a Statement? 1. The number 97 is prime. (Statement.) 2. The number 97 is a twin prime. (Statement.) 3. Which of the following is a statement? (Not a statement.) ∞ 1 ∑ 4. All zeros of the Riemann Zeta function ζ ( z ) = n z lie n = 1 on the straight line ℜ ( z ) = 1 2. (Statement.) logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Following is a Statement? 1. The number 97 is prime. (Statement.) 2. The number 97 is a twin prime. (Statement.) 3. Which of the following is a statement? (Not a statement.) ∞ 1 ∑ 4. All zeros of the Riemann Zeta function ζ ( z ) = n z lie n = 1 on the straight line ℜ ( z ) = 1 2. (Statement.) 5. c 2 = a 2 + b 2 − 2 ab cos ( γ ) . logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Following is a Statement? 1. The number 97 is prime. (Statement.) 2. The number 97 is a twin prime. (Statement.) 3. Which of the following is a statement? (Not a statement.) ∞ 1 ∑ 4. All zeros of the Riemann Zeta function ζ ( z ) = n z lie n = 1 on the straight line ℜ ( z ) = 1 2. (Statement.) 5. c 2 = a 2 + b 2 − 2 ab cos ( γ ) . (Not a statement.) logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Statements We Gave are True? logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Statements We Gave are True? 1. The number 97 is prime. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Statements We Gave are True? 1. The number 97 is prime. (True statement.) logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Statements We Gave are True? 1. The number 97 is prime. (True statement.) 2. The number 97 is a twin prime. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Statements We Gave are True? 1. The number 97 is prime. (True statement.) 2. The number 97 is a twin prime. (False statement.) logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Statements We Gave are True? 1. The number 97 is prime. (True statement.) 2. The number 97 is a twin prime. (False statement.) ∞ 1 ∑ 3. All zeros of the Riemann Zeta function ζ ( z ) = n z lie n = 1 on the straight line ℜ ( z ) = 1 2. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements

Definition Examples Truth Values Which of the Statements We Gave are True? 1. The number 97 is prime. (True statement.) 2. The number 97 is a twin prime. (False statement.) ∞ 1 ∑ 3. All zeros of the Riemann Zeta function ζ ( z ) = n z lie n = 1 on the straight line ℜ ( z ) = 1 2. (We don’t know. This is called the Riemann Hypothesis.) logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Statements