@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 youโre done. ๐(๐)

is not a group. If the operation is associative, then proceed toโฆ

Test 1: Does the set ๐(๐)

contains an identity? If you have a candidate function in ๐(๐), then what equations must it satisfy? Does it? If not, then ๐(๐)

is not a group. If you do have an identity, then proceed toโฆ

Test 2: Does every element of ๐(๐)

have an inverse? Given an arbitrary function in ๐โ๐(๐), can you write down its inverse ๐โ1โ๐(๐)? What equation must ๐ and ๐โ1 satisfy? (Hint: you need the identity function.) If any function fails to have an inverse, then ๐(๐)

is not a group. If every function does have an inverse, thenโฆ

Congratulations! Your set ๐(๐)

is a group.

Reff