implication for every integ
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
Help me with 6.18
![6.21, Pmye 41 (5" - 1) for every 1
subnl
By the Principle of Mathematical Induction, it fo
n that if |A| =
= n, then |P(A)| = 2".
%3D
(02)
Of course, Theorem 6.16 could also be stated a
The number of subsets of a finite set with n ele
SECTION 6.2 EXERCISES
CILTE OE WVHEW
6.17. Prove Theorem 6.7: For each integer m, the set S {i e Z: i>m
la subset T of S, either T CN or T N is a finite nonempty set.]M
Ds nouubai leo
r boc
6.18. Prove that 2" > n³ for every integer n > 10.
0.19. Prove the following implication for every integer n > 2: If x1, X2, -
0, then at least one of the numbers x1, X2, ... , Xp
X1. X2 X, =
%3D
two real numbers is 0, then at least one of the numbers is 0.)
0.20. (a) Use mathematical induction
element.
to prove that every finite nonemp
bms st
Use (a) to prove that every finite nonempty set of real numbe
Yo that 4 1 (5" -1) for every nonnegative integer n.
6.21. Prove tht](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F690bc708-737a-4036-8bde-cd8ee17ec8dd%2F7548f082-01da-4f4d-8873-6451c5f4afbb%2Fen3c58o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6.21, Pmye 41 (5" - 1) for every 1
subnl
By the Principle of Mathematical Induction, it fo
n that if |A| =
= n, then |P(A)| = 2".
%3D
(02)
Of course, Theorem 6.16 could also be stated a
The number of subsets of a finite set with n ele
SECTION 6.2 EXERCISES
CILTE OE WVHEW
6.17. Prove Theorem 6.7: For each integer m, the set S {i e Z: i>m
la subset T of S, either T CN or T N is a finite nonempty set.]M
Ds nouubai leo
r boc
6.18. Prove that 2" > n³ for every integer n > 10.
0.19. Prove the following implication for every integer n > 2: If x1, X2, -
0, then at least one of the numbers x1, X2, ... , Xp
X1. X2 X, =
%3D
two real numbers is 0, then at least one of the numbers is 0.)
0.20. (a) Use mathematical induction
element.
to prove that every finite nonemp
bms st
Use (a) to prove that every finite nonempty set of real numbe
Yo that 4 1 (5" -1) for every nonnegative integer n.
6.21. Prove tht
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