Set S has three elements. If you re-label {2} as A and {1,2} as B, then S={1,A,B}
Form the subsets of S from these symbols.
Then ...
replace A and B with {2} and {1,2} respectively. What do you have?
Let = {1,{2},{1,2}}.
My book says the following are subsets of : {1}, {1,{2}}, {{1,2}}
I know that 1 , {2}, {1,2} are elements of S and that {2} and {1,2} are subsets of , but I have trouble undestanding why {1}, {1,{2}}, and {{1,2}} are being subsets of . The sets {1}, {1,{2}}, and {{1,2}} seem to me are the subsets of the power set of , .
I am so confused.
Someone please help.
S={1,A,B}
3 elements, 8 subsets
{ }
{1}, {A}, {B}
{1,A}, {1,B}, {A,B}
{1,A,B}
replace A and B
(extra spaces added for emphasis -- look carefully at brackets.)
{ }
{1}, ( {2} }, { (1,2} }
{1, {2} }, {1, {1,2} } , { {2} , {1,2} }
{ 1, {2}, {1,2} }
Do you see the sets you are looking for?
I understand it fully now.
My problem being that I did not look at the definition carefully.
Following the definition, I piece them together as follows:
{1} , since 1 {1} and 1 ,
Next, {1,{2}} , since 1, {2} {1,{2}} and 1, {2} ,
Last, {{1,2}} , since {1,2} {{1,2}} and {1,2} .
I realized that the above is not exhaustive, since I can come up with more subsets, such as
{{2}{1,2}} .
Thanks you, Plato. Nice to know that you are not too far to reach.
[quote=novice;446392]Got it now after plenty of sleep. 1 and {1} imply {1}
Manx, you are a good friend because you put up with me.[/quote
technically saying {1} E S is wrong. 1 E S given S {1,{2}, {1,2}}. {1} isnt an element of S. but i think i know where your confusion comes from. a subset gets {} regardless so {1} represents the 1 in S. {{2}} represents the {2} in S and {1,{2}} represents the 1,{2} in S. on a test if you say {1} E S that would be wrong because there is no element {1} in S there IS an element of 1 in S. Saying that there is a {1} E S means that this would be S {{1},{2},{1,2}} saying 1 E S is saying there is a 1 in S which there is {1,{2},{1,2}}