Given set S={1,{a,c},b,c}?

hi, i have no idea how to do this, can someone help me with it?





given set S={1,{a,c},b,c} Find:





- all the subsets of S


- all the proper subsets of S





Thanks

Given set S={1,{a,c},b,c}?
Subset of s={ {1}, {a,c}, {b}, {c}, {1,(a,c)}, {1,b}, {1,c}, {(a,c),b},{(a,c),c}, {b,c}, {1,(a,c),b}, {1,(a,c),c}, {(a,c),b,c}, {1,{a,c},b,c},{ } }


Proper subsets of S={ {1}, {a,c}, {b}, {c}, {1,(a,c)}, {1,b}, {1,c}, {(a,c),b},{(a,c),c}, {b,c}, {1,(a,c),b}, {1,(a,c),c}, {(a,c),b,c} }


Hei! Im not sure whether nullset is a proper subset or not
Reply:-subsets of S =%26gt; { },{1},{{a,b}},{b},{C}





- all the proper subsets of S


=%26gt;





{ }


{1,{a,c},b,c}


{1}


{1,{a,c}}


{1,c}


{1,b}


{1,{a,c},b}


{1,{a,c},c}


{1,b,c}


{{a,c}}


{{a,c},b}


{{a,c},c}


{{a,c},b,c}


{b}


{b,c}


{c}


{1,{a,c},b,c}
Reply:For a list of all the proper subsets of S, list all sets with 1 element , for example {1}, {{a,c}}, {b}, {c}


Now list all sets with 2 elements.


{1, {a,c} }, { 1, c } -- finish all combinations.


Now list all sets with 3 elements.


{1, {a,c} , b} -- finish all combinations.


Note that {a,c} is 1 element even though it is a set.





For a list of all subsets:


First list all proper subsets above.


Add the set : {1, {a,c}, b, c }


This original set is a subset of itself.





We also have the nullset Φ. But it is implied that the null set is a subset of every set and you can forget about it.

forsythia