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Determine whether the relation R on the set of all Web
pages is reflexive, Irreflexive, symmetric, antisymmetric, and/or transitive,
where (a, b) ∈ R if and only if
a) everyone who has visitedWeb page a has also visited
Web page b.
b) there are no common links found on both Web
page a andWeb page b.
c) there is at least one common link onWeb page a and
Web page b.
d) there is a Web page that includes links to both Web
page a andWeb page b.

Why option a is not symmetric but reflexive? why option c and d is not reflexive?
Please explain it with clear example. Thank you.

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(a)

1) reflexive :Everyone who has visited web page a also has visited web page a

2) symmetric: There  are web pages a and b such that the set people who have visited web page a also visited web page b but there may be other people visiting web page b may not have visited web page a (e.g., depends on links between web page a and web page b). so not symmetric
3) anti symmetric: It is conceivable that there are the same set of visitors for web page a and b. so not anti symmetric.
4) transitive :If everyone who has visited a has visited b and everyone who has visited b has visited c implies that everyone who has visited a has visited c. so transitive

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If any website contains any link then the relation holds for that page (as the link is common to itself) making the relation irreflexive. Only if we restrict the domain of webpages to those without any links, the relation will be irreflexive.

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