hautiar zona plny one or none -s to 45 (no plin is 215). a) Define the notion of
ID: 3559134 • Letter: H
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hautiar zona plny one or none -s to 45 (no plin is 215). a) Define the notion of an algorithm. a finite det of seeps uued to solve a oblem b) How do algorithms differ from processes? em aud pue2 onthms oreaut, mack ane. based a2ks a) How does Injective (m,n) mathematically relate to permutation(m,n)? Using these two functions, give a mathematical equation for your answer. permutation m 1.1 l) How bea orto Partition(m,n)? these functions, give a mathematically relate to g two mathematical equation for your answer ONTOExplanation / Answer
11 (a) Algorithm: A process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer.In computer programming, algorithms are often created as functions. These functions serve as small programs that can be referenced by a larger programs.
11(b)- Algorithms terminate in a finite number of steps. Algorithm tells us a way of how a given task can be completed but a process is running program. which means in a process one or many algorithms might have been implemented with following a proper syntax of a programming language.
12(a)- Injective(m,n) means if we have two sets A with m number of elements and B with n number of elements in it then for every element of set A there must be a unique matching of it in set B. So for first element of set A we can have any one from n number of elements to be matched with this element.
So for first element we have choices =n
but when we want to make a match of element from set A to set B
then we have total elements available with us= n-1
(because one lement has already been occupied by first element)
similarly for 3rd element matches available= n-2
for 4th element matches available = n-3
................
for mth lelemnt matches available= n-m+1
so injective(m,n)= n * (n-1) * (n-2) ...............,* (n-m+1)
which is same as permutaion(m,n) = n*(n-1)*((n-2)......................*(n-m+1)
12(b)- A surjective function is one in which for every element in set B we have at least one match in set A
again consider set A has m elements
and set B has n elements
since each n elements must have at least one match in A
for 1st element of B we can ahve anyone from m elements,
for 2nd element of B we can have anyone from m-1 elements,
for 3rd element of B we can have nay one from m-2 elements,
.........................................................
for nth elements of B we can have one from , m-n+1 elements,
so this equation leads us to same as Partition(m,n)
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