9 Replies  4571 Views  Last Post: 11 April 2012  06:24 AM
#1
Please help me solve the following relation containing empty sets
Posted 11 April 2012  12:01 AM
of the second coordinate, and R ⊆ X × X.
Please help me in finding all the elements of R in list notation.
Replies To: Please help me solve the following relation containing empty sets
#2
Re: Please help me solve the following relation containing empty sets
Posted 11 April 2012  12:07 AM
#3
Re: Please help me solve the following relation containing empty sets
Posted 11 April 2012  03:04 AM
sepp2k, on 11 April 2012  12:07 AM, said:
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.
#4
Re: Please help me solve the following relation containing empty sets
Posted 11 April 2012  03:10 AM
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Yapp, that looks right.
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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
Re: Please help me solve the following relation containing empty sets
Posted 11 April 2012  03:57 AM
sepp2k, on 11 April 2012  03:10 AM, said:
Quote
Yapp, that looks right.
Quote
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
Re: Please help me solve the following relation containing empty sets
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
Yapp, that looks right.
Quote
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
Re: Please help me solve the following relation containing empty sets
Posted 11 April 2012  06:17 AM
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
Re: Please help me solve the following relation containing empty sets
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
Yapp, that looks right.
Quote
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
Re: Please help me solve the following relation containing empty sets
Posted 11 April 2012  06:23 AM
#10
Re: Please help me solve the following relation containing empty sets
Posted 11 April 2012  06:24 AM
