S = {0,1,2,3,4,5} P(S)* be the set of all nonempty subsets of S a function m: P(S)* -> S by m(H) = the largest element in H (a) Is m one-to-one? Why or why not? P(s) having n=2^6-1 element and S having m= 6 element function m is not one to one since n>m. (n be less then or equal to m ) M is not one to one since {1,3} will map to 3 {2,3} will also map tp 3 // by defination of m two element having same mapping.(IT shd be unique for each element). Does m map P(S)* onto S? Why or why not? yes m is onto funtion max element of P(s) will be in s since P(s) in subset of S only. therefore for all the element present in s will be mapping of atleat one element present in P(s). Solution S = {0,1,2,3,4,5} P(S)* be the set of all nonempty subsets of S a function m: P(S)* -> S by m(H) = the largest element in H (a) Is m one-to-one? Why or why not? P(s) having n=2^6-1 element and S having m= 6 element function m is not one to one since n>m. (n be less then or equal to m ) M is not one to one since {1,3} will map to 3 {2,3} will also map tp 3 // by defination of m two element having same mapping.(IT shd be unique for each element). Does m map P(S)* onto S? Why or why not? yes m is onto funtion max element of P(s) will be in s since P(s) in subset of S only. therefore for all the element present in s will be mapping of atleat one element present in P(s)..

1. S = {0,1,2,3,4,5}
P(S)* be the set of all nonempty subsets of S
a function m: P(S)* -> S by m(H) = the largest element in H
(a) Is m one-to-one? Why or why not?
P(s) having n=2^6-1 element
and S having m= 6 element
function m is not one to one since n>m. (n be less then or equal to m )
M is not one to one since
{1,3} will map to 3
{2,3} will also map tp 3 // by defination of m
two element having same mapping.(IT shd be unique for each element).
Does m map P(S)* onto S? Why or why not?
yes m is onto funtion
max element of P(s) will be in s since P(s) in subset of S only.
therefore for all the element present in s will be mapping of atleat one element present in P(s).
Solution

2. S = {0,1,2,3,4,5}
P(S)* be the set of all nonempty subsets of S
a function m: P(S)* -> S by m(H) = the largest element in H
(a) Is m one-to-one? Why or why not?
P(s) having n=2^6-1 element
and S having m= 6 element
function m is not one to one since n>m. (n be less then or equal to m )
M is not one to one since
{1,3} will map to 3
{2,3} will also map tp 3 // by defination of m
two element having same mapping.(IT shd be unique for each element).
Does m map P(S)* onto S? Why or why not?
yes m is onto funtion
max element of P(s) will be in s since P(s) in subset of S only.
therefore for all the element present in s will be mapping of atleat one element present in P(s).