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Why is this relation not reflexive?
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Determine whether the relation R on the set of all Web
pages is reflexive, symmetric, antisymmetric, and/or transitive,
where (a, b) ∈ R if and only if
there is at least one common link onWeb page a and
Web page b.
Why is this relation not reflexive?
discrete-mathematics relations
asked Jul 31 at 15:19
i11_1997
132
add a comment |Â
up vote
0
down vote
favorite
Determine whether the relation R on the set of all Web
pages is reflexive, symmetric, antisymmetric, and/or transitive,
where (a, b) ∈ R if and only if
there is at least one common link onWeb page a and
Web page b.
Why is this relation not reflexive?
discrete-mathematics relations
asked Jul 31 at 15:19
i11_1997
132
1
Note that, perhaps somewhat counterintuitively, the seemingly stronger condition that the pages have all their links in common does yield a reflexive relation (in fact an equivalence relation).
– joriki
Jul 31 at 15:24
1
If a web page has any link at all, then it has a link in common with itself and thus is related to itself. But if a web page has no links at all then it doesnt have any links in common with itself and is no related to itself (or to any page). So either a page is related to itself or it has no links. But having no links is an option. (It's clearly symmetric [and not anti-symmetric] though, and easily seen to not be transitive.)
– fleablood
Jul 31 at 15:41
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Determine whether the relation R on the set of all Web
pages is reflexive, symmetric, antisymmetric, and/or transitive,
where (a, b) ∈ R if and only if
there is at least one common link onWeb page a and
Web page b.
Why is this relation not reflexive?
discrete-mathematics relations
asked Jul 31 at 15:19
i11_1997
132
Determine whether the relation R on the set of all Web
pages is reflexive, symmetric, antisymmetric, and/or transitive,
where (a, b) ∈ R if and only if
there is at least one common link onWeb page a and
Web page b.
Why is this relation not reflexive?
discrete-mathematics relations
asked Jul 31 at 15:19
i11_1997
132
asked Jul 31 at 15:19
i11_1997
132
asked Jul 31 at 15:19
i11_1997
132
asked Jul 31 at 15:19
i11_1997
132
132
1
Note that, perhaps somewhat counterintuitively, the seemingly stronger condition that the pages have all their links in common does yield a reflexive relation (in fact an equivalence relation).
– joriki
Jul 31 at 15:24
1
If a web page has any link at all, then it has a link in common with itself and thus is related to itself. But if a web page has no links at all then it doesnt have any links in common with itself and is no related to itself (or to any page). So either a page is related to itself or it has no links. But having no links is an option. (It's clearly symmetric [and not anti-symmetric] though, and easily seen to not be transitive.)
– fleablood
Jul 31 at 15:41
add a comment |Â
1
Note that, perhaps somewhat counterintuitively, the seemingly stronger condition that the pages have all their links in common does yield a reflexive relation (in fact an equivalence relation).
– joriki
Jul 31 at 15:24
1
If a web page has any link at all, then it has a link in common with itself and thus is related to itself. But if a web page has no links at all then it doesnt have any links in common with itself and is no related to itself (or to any page). So either a page is related to itself or it has no links. But having no links is an option. (It's clearly symmetric [and not anti-symmetric] though, and easily seen to not be transitive.)
– fleablood
Jul 31 at 15:41
1
1
Note that, perhaps somewhat counterintuitively, the seemingly stronger condition that the pages have all their links in common does yield a reflexive relation (in fact an equivalence relation).
– joriki
Jul 31 at 15:24
Note that, perhaps somewhat counterintuitively, the seemingly stronger condition that the pages have all their links in common does yield a reflexive relation (in fact an equivalence relation).
– joriki
Jul 31 at 15:24
1
1
If a web page has any link at all, then it has a link in common with itself and thus is related to itself. But if a web page has no links at all then it doesnt have any links in common with itself and is no related to itself (or to any page). So either a page is related to itself or it has no links. But having no links is an option. (It's clearly symmetric [and not anti-symmetric] though, and easily seen to not be transitive.)
– fleablood
Jul 31 at 15:41
If a web page has any link at all, then it has a link in common with itself and thus is related to itself. But if a web page has no links at all then it doesnt have any links in common with itself and is no related to itself (or to any page). So either a page is related to itself or it has no links. But having no links is an option. (It's clearly symmetric [and not anti-symmetric] though, and easily seen to not be transitive.)
– fleablood
Jul 31 at 15:41
add a comment |Â
1 Answer
1
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2
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Because a webpage can have no links.
answered Jul 31 at 15:19
Kenny Lau
17.7k2156
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
Because a webpage can have no links.
answered Jul 31 at 15:19
Kenny Lau
17.7k2156
add a comment |Â
up vote
2
down vote
Because a webpage can have no links.
answered Jul 31 at 15:19
Kenny Lau
17.7k2156
add a comment |Â
up vote
2
down vote
up vote
2
down vote
Because a webpage can have no links.
answered Jul 31 at 15:19
Kenny Lau
17.7k2156
Because a webpage can have no links.
answered Jul 31 at 15:19
Kenny Lau
17.7k2156
answered Jul 31 at 15:19
Kenny Lau
17.7k2156
answered Jul 31 at 15:19
Kenny Lau
17.7k2156
answered Jul 31 at 15:19
Kenny Lau
17.7k2156
17.7k2156
add a comment |Â
add a comment |Â
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1
Note that, perhaps somewhat counterintuitively, the seemingly stronger condition that the pages have all their links in common does yield a reflexive relation (in fact an equivalence relation).
– joriki
Jul 31 at 15:24
1
If a web page has any link at all, then it has a link in common with itself and thus is related to itself. But if a web page has no links at all then it doesnt have any links in common with itself and is no related to itself (or to any page). So either a page is related to itself or it has no links. But having no links is an option. (It's clearly symmetric [and not anti-symmetric] though, and easily seen to not be transitive.)
– fleablood
Jul 31 at 15:41