@zareen said in MTH633 Assignment 1 Solution and Discussion:
Write down the elements of group under composition
Test 0: Is the operation associative? If not, then youβre done. π(π)
is not a group. If the operation is associative, then proceed toβ¦
Test 1: Does the set π(π)
contains an identity? If you have a candidate function in π(π), then what equations must it satisfy? Does it? If not, then π(π)
is not a group. If you do have an identity, then proceed toβ¦
Test 2: Does every element of π(π)
have an inverse? Given an arbitrary function in πβπ(π), can you write down its inverse πβ1βπ(π)? What equation must π and πβ1 satisfy? (Hint: you need the identity function.) If any function fails to have an inverse, then π(π)
is not a group. If every function does have an inverse, thenβ¦
Congratulations! Your set π(π)
is a group.
Reff
