# Answer to Question #15485 in Abstract Algebra for Sujata Roy

Question #15485

A partial order <= is defined on the set S = {x,a1,a2,...,an,y} as x<=ai for all i and ai<=y for all i, where n>=1. Number of total orders on the set S which contain partial order <= is

a) 1

b) n

c) n+2

d) n!

a) 1

b) n

c) n+2

d) n!

Expert's answer

We fix only minimal and maximal element, so positions of other n element are

arbitrary.

Number of total orders coincide with number of permutations of set

{1,2,...,n}, since every total order can be interpreted as n-tuple of elements

a_i.

Thus as it is well-known there are n! different permutations of set

{1,2,...,n}. So answer is d)

arbitrary.

Number of total orders coincide with number of permutations of set

{1,2,...,n}, since every total order can be interpreted as n-tuple of elements

a_i.

Thus as it is well-known there are n! different permutations of set

{1,2,...,n}. So answer is d)

## Comments

Assignment Expert01.10.12, 14:13You're welcome. We are glad to be helpful.

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Sujata Roy28.09.12, 22:06thank you sir..

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