[anlokri]

X = {ø, {ø}, {{ø}}} and R = ⊆ (R is the relation of all ordered pairs where each first co-ordinate is a subset
of the second co-ordinate, and R ⊆ X × X.

Please help me in finding all the elements of R in list notation.

[sepp2k]

The set X has 3 elements. So compare each of those elements to each other element and to itself to see whether it's a subset. If element x is a subset of element y, the pair (x,y) will be in R. If not it won't. Once you did this for all 3*3 pairs of elements, you know all the elements in R.

[anlokri]

sepp2k, on 11 April 2012 - 12:07 AM, said:

The set X has 3 elements. So compare each of those elements to each other element and to itself to see whether it's a subset. If element x is a subset of element y, the pair (x,y) will be in R. If not it won't. Once you did this for all 3*3 pairs of elements, you know all the elements in R.

Thanks for you help. Would the answer be R = {(ø,ø), (ø,{ø}), (ø,{{ø}}), ({ø}{ø}), ({{ø}},{{ø}})}? Because 1st coordinate must be subset of 2nd coordinate.

Is it true that ({ø},{{ø}}) is not an element of R as shown above. Is {ø} not a subset of {{ø}}?

Thanks again for your help.

[sepp2k]

Quote

Thanks for you help. Would the answer be R = {(ø,ø), (ø,{ø}), (ø,{{ø}}), ({ø}{ø}), ({{ø}},{{ø}})}? Because 1st coordinate must be subset of 2nd coordinate.

Yapp, that looks right.

Quote

Is it true that ({ø},{{ø}}) is not an element of R as shown above. Is {ø} not a subset of {{ø}}?

That's correct. {ø} contains ø as an element. {{ø}} does not contain ø as an element. So {ø} can't be subset of {{ø}} (it is an element of {{ø}} though, but that doesn't matter for the question).

[anlokri]

sepp2k, on 11 April 2012 - 03:10 AM, said:

Quote

Thanks for you help. Would the answer be R = {(ø,ø), (ø,{ø}), (ø,{{ø}}), ({ø}{ø}), ({{ø}},{{ø}})}? Because 1st coordinate must be subset of 2nd coordinate.

Yapp, that looks right.

Quote

Is it true that ({ø},{{ø}}) is not an element of R as shown above. Is {ø} not a subset of {{ø}}?

That's correct. {ø} contains ø as an element. {{ø}} does not contain ø as an element. So {ø} can't be subset of {{ø}} (it is an element of {{ø}} though, but that doesn't matter for the question).

Thank you, appreciate it!

[anlokri]

anlokri, on 11 April 2012 - 03:57 AM, said:

sepp2k, on 11 April 2012 - 03:10 AM, said:

Quote

Thanks for you help. Would the answer be R = {(ø,ø), (ø,{ø}), (ø,{{ø}}), ({ø}{ø}), ({{ø}},{{ø}})}? Because 1st coordinate must be subset of 2nd coordinate.

Yapp, that looks right.

Quote

Is it true that ({ø},{{ø}}) is not an element of R as shown above. Is {ø} not a subset of {{ø}}?

That's correct. {ø} contains ø as an element. {{ø}} does not contain ø as an element. So {ø} can't be subset of {{ø}} (it is an element of {{ø}} though, but that doesn't matter for the question).

Thank you, appreciate it!

Just for interest sake. Because {ø} contains ø as an element and {{ø}} does not contain ø as an element can {{ø}} be a subset of {ø}?

[sepp2k]

For x to be subset of y, y needs to contain all elements that x contains. In the case of {ø} and {{ø}}, both contain an element that the other one does not ({ø} contains ø and {{ø}} contains {ø}), so neither is a subset or a superset of the other.

Also if you have two sets that have the same number of elements (as you do here), the only way one is a subset of the other is if both sets are equal.

[anlokri]

anlokri, on 11 April 2012 - 06:12 AM, said:

anlokri, on 11 April 2012 - 03:57 AM, said:

sepp2k, on 11 April 2012 - 03:10 AM, said:

Quote

Thanks for you help. Would the answer be R = {(ø,ø), (ø,{ø}), (ø,{{ø}}), ({ø}{ø}), ({{ø}},{{ø}})}? Because 1st coordinate must be subset of 2nd coordinate.

Yapp, that looks right.

Quote

Is it true that ({ø},{{ø}}) is not an element of R as shown above. Is {ø} not a subset of {{ø}}?

That's correct. {ø} contains ø as an element. {{ø}} does not contain ø as an element. So {ø} can't be subset of {{ø}} (it is an element of {{ø}} though, but that doesn't matter for the question).

Thank you, appreciate it!

Just for interest sake. Because {ø} contains ø as an element and {{ø}} does not contain ø as an element can {{ø}} be a subset of {ø}?

Will it be correct if I reason that {{ø}} can NOT be a subset of {ø} because {{ø}} would have the element {ø} which is not found in the set {ø}?

[sepp2k]

Yes, that is correct.

[anlokri]

Thanks again for your help, I now have a much better idea of building subsets from sets containing sets with ø.