given quantity. (See Example 2.) 7. the sum of an even integer and an odd integer
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
7
![In Exercises 1-6, describe the pattern. Then write
or 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 the
given quantity. (See Example 2.)
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
In Exercises 11-14, find a counterexample to show that
the conjecture is false. (See Example 3.)
11. The product of two positive numbers is always greater
than either number.
x+1
71
12. If n is a nonzero integer, then 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 s divides MN into two line segments. So, the
line s is a segment bisector of MN.
In Exercises 15-18, use the Law of Detachment to
determine what you can conclude from the given
information, 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 go
to the mountains with your friend. You will go to the
mountains with your friend.
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 L.H into two congruent line segments.
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. 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 a
parallelogram. If a figure is a parallelogram, then
the figure has two pairs of opposite sides that
are parallel.
22. If a figure is a square, then the figure has four
congruent sides. If a figure is a square, then the
figure has four right angles.
In Exercises 23-26, state the law of logic that
is illustrated.
23. If you do your homework, then you can watch TV. If
you watch TV, then you can watch your favorite show.
If you do your homework, then you can watch your
favorite show.
24. If you miss practice the day before a game, then you
will not be a starting player in the game.
You miss practice on Tuesday. You will not start the
game 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 to
make a conjecture about the given quantity. Then use
deductive reasoning to show that the conjecture is true.
(See Example 6.)
27. the sum of two add integers
28. the product of two odd integers
GO DIGITAL](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F190d6977-2ae2-4a51-aa5b-fbc1e2d73150%2Fef16001f-c822-4441-85e5-98a9f3fe0174%2F1udg2ye_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In Exercises 1-6, describe the pattern. Then write
or 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 the
given quantity. (See Example 2.)
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
In Exercises 11-14, find a counterexample to show that
the conjecture is false. (See Example 3.)
11. The product of two positive numbers is always greater
than either number.
x+1
71
12. If n is a nonzero integer, then 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 s divides MN into two line segments. So, the
line s is a segment bisector of MN.
In Exercises 15-18, use the Law of Detachment to
determine what you can conclude from the given
information, 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 go
to the mountains with your friend. You will go to the
mountains with your friend.
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 L.H into two congruent line segments.
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. 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 a
parallelogram. If a figure is a parallelogram, then
the figure has two pairs of opposite sides that
are parallel.
22. If a figure is a square, then the figure has four
congruent sides. If a figure is a square, then the
figure has four right angles.
In Exercises 23-26, state the law of logic that
is illustrated.
23. If you do your homework, then you can watch TV. If
you watch TV, then you can watch your favorite show.
If you do your homework, then you can watch your
favorite show.
24. If you miss practice the day before a game, then you
will not be a starting player in the game.
You miss practice on Tuesday. You will not start the
game 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 to
make a conjecture about the given quantity. Then use
deductive reasoning to show that the conjecture is true.
(See Example 6.)
27. the sum of two add integers
28. the product of two odd integers
GO DIGITAL
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