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Page 1L2 Supplementary Notes
04-02-2010: Recap
Sum Principle Applied to selection sort
Product Principle Applied to matrix multiplication and the next item
Two element-subsets
Set concepts and notations Sets, mutually disjoint sets, size, union, partition Set does not allow duplicates
Page 3L2 Supplementary Notes
04-02-2010 Recap: Product Principle
Si and Sj are disjoint, |Si| = n
S = S1 U S2 U … U Sm
|S| = m |Si| = mn
Page 9L2 Supplementary Notes
Discrete Function (MC 11, 12)
S = {1, 2, 3}: domain of function f
T={Sam, Mary, Sarah}: range of function f
Page 10L2 Supplementary Notes
Notes (MC 11)
For each element s of S, f gives one element of T, f(s)
In general NOT: For each element of T,…
There may be t of T, such that f(s) \= t for all s of S
Only a special kind of function has this property, onto
Page 20L2 Supplementary Notes
Bijection Principle
Counting elements in S
May be difficult directly
Find another set T that is easy to count
Define a function f: S T
Prove that f is a bijection
Count T