Answer to Question #105584 in Abstract Algebra for Sourav Mondal

Question

Obtain the order of each element of ℘(S) where S={1,2,3}

Answer 1

$P(S)=$ { {1},{2},{3},{1,2},{2,3},{1,3},{1,2,3},$\empty$ }

$O($ order of a set $)$ $=$number of element at that set.

Elements of set $P(S)$ are set in itself.

$O($ {1}$)=$ 1, $O($ {2}$)=2$ ,$O($ {3}$)=$ 3,$O($ {1,2}$)=$ 2, $O($ {2,3}$)=2$

$O($ {1,3}$)=$ 2 ,$O($ {1,2,3}$)=$ 3 , $O(\empty )=$ 0.