Page 1 of 1

## 9 Replies - 6882 Views - Last Post: 11 April 2012 - 06:24 AM

### #1 anlokri

Reputation: 0
• Posts: 6
• Joined: 10-April 12

Posted 11 April 2012 - 12:01 AM

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.

Is This A Good Question/Topic? 0

### #2 sepp2k

• D.I.C Lover

Reputation: 2549
• Posts: 4,069
• Joined: 21-June 11

Posted 11 April 2012 - 12:07 AM

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.

### #3 anlokri

Reputation: 0
• Posts: 6
• Joined: 10-April 12

Posted 11 April 2012 - 03:04 AM

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}}?

### #4 sepp2k

• D.I.C Lover

Reputation: 2549
• Posts: 4,069
• Joined: 21-June 11

Posted 11 April 2012 - 03:10 AM

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).

### #5 anlokri

Reputation: 0
• Posts: 6
• Joined: 10-April 12

Posted 11 April 2012 - 03:57 AM

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!

### #6 anlokri

Reputation: 0
• Posts: 6
• Joined: 10-April 12

Posted 11 April 2012 - 06:12 AM

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}?

### #7 sepp2k

• D.I.C Lover

Reputation: 2549
• Posts: 4,069
• Joined: 21-June 11

Posted 11 April 2012 - 06:17 AM

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.

### #8 anlokri

Reputation: 0
• Posts: 6
• Joined: 10-April 12

Posted 11 April 2012 - 06:17 AM

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}?

### #9 sepp2k

• D.I.C Lover

Reputation: 2549
• Posts: 4,069
• Joined: 21-June 11

Posted 11 April 2012 - 06:23 AM

Yes, that is correct.

### #10 anlokri

Reputation: 0
• Posts: 6
• Joined: 10-April 12