Let S be the set of integer solutions to the equation 1+x2+x3+£4 = 30, where x; >0 for i = 1, 2, 3, 4. That is, S = {(x1,12, X3, T4) | Xi € Z and xi > 0 and r1 + 12 + x3 + 14 = 30}. (a) Find |S]. For i = 1, 2, 3, 4, define A; = {(x1, 12, x3, X4) E S | x¿ > 10}.
Let S be the set of integer solutions to the equation 1+x2+x3+£4 = 30, where x; >0 for i = 1, 2, 3, 4. That is, S = {(x1,12, X3, T4) | Xi € Z and xi > 0 and r1 + 12 + x3 + 14 = 30}. (a) Find |S]. For i = 1, 2, 3, 4, define A; = {(x1, 12, x3, X4) E S | x¿ > 10}.
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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![1. Let S be the set of integer solutions to the equation r1+x2 + x3+x4 = 30, where x; >0 for
i = 1, 2, 3, 4. That is,
S = {(x1, x2, X3, x4) | Xi E Z and xi > 0 and x1 + x2 +x3+x4 = 30}.
(a) Find |S].
For i = 1, 2, 3, 4, define A; = {(r1, X2, X3, T4) E S | x; > 10}.
(b) Find |A¡| for each i.
(c) For each 1<i<j<4, find |A¡ N A¡|.
(d) For each 1<i<j<k<4, find |A; N A; N Ak|.
(e) Find |A1 N A2 N A3 N A4|.
(f) Find the number of integer solutions to xi + x2 + x3 + x4 = 30 with 0 < xi < 9 for
i = 1, 2, 3, 4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5ea8dc3-9812-419a-a20e-59637a068d91%2F5c8d0cf4-8bc1-43ec-996e-6bac3cf172da%2Fa9jnt9_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let S be the set of integer solutions to the equation r1+x2 + x3+x4 = 30, where x; >0 for
i = 1, 2, 3, 4. That is,
S = {(x1, x2, X3, x4) | Xi E Z and xi > 0 and x1 + x2 +x3+x4 = 30}.
(a) Find |S].
For i = 1, 2, 3, 4, define A; = {(r1, X2, X3, T4) E S | x; > 10}.
(b) Find |A¡| for each i.
(c) For each 1<i<j<4, find |A¡ N A¡|.
(d) For each 1<i<j<k<4, find |A; N A; N Ak|.
(e) Find |A1 N A2 N A3 N A4|.
(f) Find the number of integer solutions to xi + x2 + x3 + x4 = 30 with 0 < xi < 9 for
i = 1, 2, 3, 4.
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