19 In Exercises 1-6, describe the pattern. Then writeor draw the next two numbers, letters, or figures.(See Example 1.)1. 1.-2.3, -4,5....3. Z, Y. X, W, V,...▶5.6.2. 0. 2, 6, 12, 20,...4. A. D. G. J, M, …..In Exercises 7-10), make and test a conjecture about thegiven quantity. (See Example 2.)7. the sum of an even integer and an odd integer8. the product of any two even integers9. the quotient of a number and its reciprocal10. the quotient of two negative integersIn Exercises 11-14, find a counterexample to show thatthe conjecture is false. (See Example 3.)11. The product of two positive numbers is always greaterthan either number.x+17112. If n is a nonzero integer, then is always greaterthan 1.13. If two angles are supplements of each other, then oneof the angles must be acute.14. A line s divides MN into two line segments. So, theline s is a segment bisector of MN.In Exercises 15-18, use the Law of Detachment todetermine what you can conclude from the giveninformation, if possible. (See Example 4.)15. If you download a GIF, then your device crashes.You download a GIF.16. If your cousin lets you borrow a car, then you will goto the mountains with your friend. You will go to themountains with your friend.17. If a quadrilateral is a square, then it has four rightangles. Quadrilateral QRST has four right angles.18. If a point divides a line segment into two congruentline segments, then the point is a midpoint, Point Pdivides L.H into two congruent line segments.In Exercises 19-22, use the Law of Syllogism to write anew conditional statement that follows from the pair oftrue statements, if possible. (See Example 5.)19. Ifx-2, then |x| 2. If x 2, then |x| 2.20. If a = 3, then 5o = 15. If / 2 = 1, then a = 3.21. If a figure is a rhombus, then the figure is aparallelogram. If a figure is a parallelogram, thenthe figure has two pairs of opposite sides thatare parallel.22. If a figure is a square, then the figure has fourcongruent sides. If a figure is a square, then thefigure has four right angles.In Exercises 23-26, state the law of logic thatis illustrated.23. If you do your homework, then you can watch TV. Ifyou watch TV, then you can watch your favorite show.If you do your homework, then you can watch yourfavorite show.24. If you miss practice the day before a game, then youwill not be a starting player in the game.You miss practice on Tuesday. You will not start thegame Wednesday.25. Ifx 12, then x +9 20. The value of x is 14.So.x+9 20.26. If I and 2 are vertical angles, then Z1 = 22.If 41 = 22. then mx21 = m22.If 21 and 22 are vertical angles, then m1 = 22.In Exercises 27 and 28, use inductive reasoning tomake a conjecture about the given quantity. Then usedeductive reasoning to show that the conjecture is true.(See Example 6.)27. the sum of two add integers28. the product of two odd integersGO DIGITAL

Question

19 In Exercises 1-6, describe the pattern. Then writeor draw the next two numbers, letters, or figures.(See Example 1.)1. 1.-2.3, -4,5....3. Z, Y. X, W, V,...▶5.6.2. 0. 2, 6, 12, 20,...4. A. D. G. J, M, …..In Exercises 7-10), make and test a conjecture about thegiven quantity. (See Example 2.)7. the sum of an even integer and an odd integer8. the product of any two even integers9. the quotient of a number and its reciprocal10. the quotient of two negative integersIn Exercises 11-14, find a counterexample to show thatthe conjecture is false. (See Example 3.)11. The product of two positive numbers is always greaterthan either number.x+17112. If n is a nonzero integer, then is always greaterthan 1.13. If two angles are supplements of each other, then oneof the angles must be acute.14. A line s divides MN into two line segments. So, theline s is a segment bisector of MN.In Exercises 15-18, use the Law of Detachment todetermine what you can conclude from the giveninformation, if possible. (See Example 4.)15. If you download a GIF, then your device crashes.You download a GIF.16. If your cousin lets you borrow a car, then you will goto the mountains with your friend. You will go to themountains with your friend.17. If a quadrilateral is a square, then it has four rightangles. Quadrilateral QRST has four right angles.18. If a point divides a line segment into two congruentline segments, then the point is a midpoint, Point Pdivides L.H into two congruent line segments.In Exercises 19-22, use the Law of Syllogism to write anew conditional statement that follows from the pair oftrue statements, if possible. (See Example 5.)19. Ifx-2, then |x|> 2. If x > 2, then |x|> 2.20. If a = 3, then 5o = 15. If / 2 = 1, then a = 3.21. If a figure is a rhombus, then the figure is aparallelogram. If a figure is a parallelogram, thenthe figure has two pairs of opposite sides thatare parallel.22. If a figure is a square, then the figure has fourcongruent sides. If a figure is a square, then thefigure has four right angles.In Exercises 23-26, state the law of logic thatis illustrated.23. If you do your homework, then you can watch TV. Ifyou watch TV, then you can watch your favorite show.If you do your homework, then you can watch yourfavorite show.24. If you miss practice the day before a game, then youwill not be a starting player in the game.You miss practice on Tuesday. You will not start thegame Wednesday.25. Ifx> 12, then x +9> 20. The value of x is 14.So.x+9> 20.26. If I and 2 are vertical angles, then Z1 = 22.If 41 = 22. then mx21 = m22.If 21 and 22 are vertical angles, then m1 = 22.In Exercises 27 and 28, use inductive reasoning tomake a conjecture about the given quantity. Then usedeductive reasoning to show that the conjecture is true.(See Example 6.)27. the sum of two add integers28. the product of two odd integersGO DIGITAL

Accepted Answer

we need to find the new conditional statement.

In Exercises 19-22, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements, if possible. (See Example 5.) 19. Ifx-2, then x > 2. Ifx > 2, then x > 2.