Publish On: 2019-05-24

# jollay

Total Post: 559

## Question: Describe the symmetric set of degree n

Reply On: 2013-10-08

# Mjay Jollay

Total Post: 0

## ANS: Describe the symmetric set of degree n

If S is a finite set containing n distinct elements, then there will be n! distinct arrangements of the elements of set S. The set of all these n! arrangements is denoted by S

S

Obviously, a set of three elements will have 3! Elements, i.e. S

Let S = {1, 2, 3, …., n}.

Let ƒ S

Since ƒ is one-one onto, so we have

n choices for (1)ƒ

(n – 1) choices for (2)ƒ

………….

………….

1 choice for (n)ƒ

Hence in all n(n – 1) (n – 2) …… 3.2.1. = n! functions ƒ S

_{n}and is known as symmetric set of permutations of degree n or symmetric set of degree n. AlsoS

_{n}= {ƒ : ƒ is a permutation of degree n}Obviously, a set of three elements will have 3! Elements, i.e. S

_{3}will have been 3! Or 6 elements.Let S = {1, 2, 3, …., n}.

Let ƒ S

_{n}be a permutation of S_{n}. This can be exhibited asSince ƒ is one-one onto, so we have

n choices for (1)ƒ

(n – 1) choices for (2)ƒ

………….

………….

1 choice for (n)ƒ

Hence in all n(n – 1) (n – 2) …… 3.2.1. = n! functions ƒ S

_{n}can arise. Thus S_{n}has n! elements.Like Us On Facebook for All Latest Updates