5. Number of mappings, injections, surjections: a. Counting total number of mappings from A to B (|A| = n, |B|= m) in two ways: (") : * s(n, 1) * 1! + (") * s(n, 2) * 2! + ... + (m) * s(n, m) * m! m" = Total and sliced by increasing size of the Image of the function. Must get the same answer. Verify identity for n = 7, m = 4 using your Pascal and Stirling triangles. b. Give the number of surjections (onto) maps from A to B (|A| = 3, |B|= 5). С. Find the number of injections (one to one) maps from A to B (|A| = 3, |B|= 5).
5. Number of mappings, injections, surjections: a. Counting total number of mappings from A to B (|A| = n, |B|= m) in two ways: (") : * s(n, 1) * 1! + (") * s(n, 2) * 2! + ... + (m) * s(n, m) * m! m" = Total and sliced by increasing size of the Image of the function. Must get the same answer. Verify identity for n = 7, m = 4 using your Pascal and Stirling triangles. b. Give the number of surjections (onto) maps from A to B (|A| = 3, |B|= 5). С. Find the number of injections (one to one) maps from A to B (|A| = 3, |B|= 5).
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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Transcribed Image Text:5. Number of mappings, injections, surjections:
a. Counting total number of mappings from A to B (|A| = n, |B| = m) in two ways:
(")
* s(n, 1) * 1! + (C) * s(n, 2) * 2! + ...
+ (m) * s(n, m) * m!
m" =
Total and sliced by increasing size of the Image of the function. Must get the same
answer.
Verify identity for n = 7, m = 4 using your Pascal and Stirling triangles.
b. Give the number of surjections (onto) maps from A to B (|A| = 3, |B|= 5).
С.
Find the number of injections (one to one) maps from A to B (|A| = 3, |B|= 5).
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