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17. If a quadrilateral is a square, then it has four right angles. Quadrilateral QRST has four right angles. IC

17. If a quadrilateral is a square, then it has four right angles. Quadrilateral QRST has four right angles. IC

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Mathematics Patterns and Logical Reasoning** **Patterns and Sequences** *In Exercises 1–6, describe the pattern. Then write or draw the next two numbers, letters, or figures.* 1. Sequence: -1, 2, -3, 4, -5, ... 2. Sequence: 0, 2, 6, 12, 20, ... 3. Sequence: Y, X, W, V, ... 4. Sequence: A, D, G, J, M, ... 5. Image: Sequence of shapes including a hexagon and a pentagon. 6. Image: Sequence of stacked cubes forming a pattern. **Conjectures** *In Exercises 7–10, make and test a conjecture about the given quantity.* 7. The sum of an even integer and an odd integer. 8. The product of any two even integers. 9. The quotient of a number and its reciprocal. 10. The quotient of two negative integers. **Counterexamples** *In Exercises 11–14, find a counterexample to show that the conjecture is false.* 11. The product of two positive numbers is always greater than either number. 12. If n is a nonzero integer, then \( n + \frac{1}{n} \) is always greater than 1. 13. If two angles are supplements of each other, then one of the angles must be acute. 14. A line divides segment MN into two line segments. So, the line is a segment bisector of segment MN. **Logical Deduction** *In Exercises 15–18, use the Law of Detachment to determine what you can conclude from the given information.* 15. If you download a GIF, then your device crashes. You download a GIF. 16. If you drive in traffic, then you will go slowly. You are driving in traffic. 17. If a quadrilateral is a square, then it has four right angles. Quadrilateral QRST has four right angles. 18. If a point divides a line segment into two congruent line segments, then the point is a midpoint. Point P divides FH into two congruent line segments. **Law of Syllogism** *In Exercises 19–22, use the Law of Syllogism to write a new conditional statement.* 19. If x < −2, then |x| > 2. If
Transcribed Image Text:**Mathematics Patterns and Logical Reasoning** **Patterns and Sequences** *In Exercises 1–6, describe the pattern. Then write or draw the next two numbers, letters, or figures.* 1. Sequence: -1, 2, -3, 4, -5, ... 2. Sequence: 0, 2, 6, 12, 20, ... 3. Sequence: Y, X, W, V, ... 4. Sequence: A, D, G, J, M, ... 5. Image: Sequence of shapes including a hexagon and a pentagon. 6. Image: Sequence of stacked cubes forming a pattern. **Conjectures** *In Exercises 7–10, make and test a conjecture about the given quantity.* 7. The sum of an even integer and an odd integer. 8. The product of any two even integers. 9. The quotient of a number and its reciprocal. 10. The quotient of two negative integers. **Counterexamples** *In Exercises 11–14, find a counterexample to show that the conjecture is false.* 11. The product of two positive numbers is always greater than either number. 12. If n is a nonzero integer, then \( n + \frac{1}{n} \) is always greater than 1. 13. If two angles are supplements of each other, then one of the angles must be acute. 14. A line divides segment MN into two line segments. So, the line is a segment bisector of segment MN. **Logical Deduction** *In Exercises 15–18, use the Law of Detachment to determine what you can conclude from the given information.* 15. If you download a GIF, then your device crashes. You download a GIF. 16. If you drive in traffic, then you will go slowly. You are driving in traffic. 17. If a quadrilateral is a square, then it has four right angles. Quadrilateral QRST has four right angles. 18. If a point divides a line segment into two congruent line segments, then the point is a midpoint. Point P divides FH into two congruent line segments. **Law of Syllogism** *In Exercises 19–22, use the Law of Syllogism to write a new conditional statement.* 19. If x < −2, then |x| > 2. If
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