Find the following cardinalities (Do not list the elements of the sets). A² = A x A, for any set A.) Show your work. (a) |([10]² — {1,3, 4, 5} × {2, 5, 6, 7}) — {4, 5, 6, 7} × {2, 7, 8, 9}|. (b) |(([10]² — [6]²) — {4, 5, 6, 7, 8, 9}²) — {1, 2, 4, 5, 7, 8}²|. (c) |([10]² — {1,2,5, 6, 9, 10}²) — ({2, 3, 4, 5, 6, 7, 8, 9}² — {4, 5, 6, 7}²)|
Find the following cardinalities (Do not list the elements of the sets). A² = A x A, for any set A.) Show your work. (a) |([10]² — {1,3, 4, 5} × {2, 5, 6, 7}) — {4, 5, 6, 7} × {2, 7, 8, 9}|. (b) |(([10]² — [6]²) — {4, 5, 6, 7, 8, 9}²) — {1, 2, 4, 5, 7, 8}²|. (c) |([10]² — {1,2,5, 6, 9, 10}²) — ({2, 3, 4, 5, 6, 7, 8, 9}² — {4, 5, 6, 7}²)|
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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![Find the following cardinalities (Do not list the elements of the sets). (Notation
A² = A x A, for any set A.) Show your work.
(a) ([10]² - {1,3,4,5} × {2, 5, 6, 7}) — {4, 5, 6, 7} × {2,7,8,9}|.
(b) (([10]²[6]²) - {4, 5, 6, 7, 8, 9}²) — {1, 2, 4, 5, 7, 8}²|.
(c) ([10]² - {1, 2, 5, 6, 9, 10}²) — ({2, 3, 4, 5, 6, 7, 8, 9}² — {4, 5, 6, 7}²)|
(d) {(x, y) = [10]² | x ≤ y}^{(x, y) = [10]² | y ≤ 11 − x}|
(e) (([10] × {1,3,5,7,9}) U ({1, 3, 5, 7, 9} × [10])) ^{(x, y) = [10]² | |y − x| ≤ 2}|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffc06da2-7bd8-42a3-b8a1-3f8b831a8034%2F17eebffe-5519-420b-94c5-9e16b70f53b1%2Fj89n1c8_processed.png&w=3840&q=75)
Transcribed Image Text:Find the following cardinalities (Do not list the elements of the sets). (Notation
A² = A x A, for any set A.) Show your work.
(a) ([10]² - {1,3,4,5} × {2, 5, 6, 7}) — {4, 5, 6, 7} × {2,7,8,9}|.
(b) (([10]²[6]²) - {4, 5, 6, 7, 8, 9}²) — {1, 2, 4, 5, 7, 8}²|.
(c) ([10]² - {1, 2, 5, 6, 9, 10}²) — ({2, 3, 4, 5, 6, 7, 8, 9}² — {4, 5, 6, 7}²)|
(d) {(x, y) = [10]² | x ≤ y}^{(x, y) = [10]² | y ≤ 11 − x}|
(e) (([10] × {1,3,5,7,9}) U ({1, 3, 5, 7, 9} × [10])) ^{(x, y) = [10]² | |y − x| ≤ 2}|
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