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
a) everyone who has visited Web page a has also visited Web page b.
b) there are no common links found on both Web page a and Web page b.
c) there is at least one common link on Web page a and Web page b.
d) a is taller than b.
e) a and b were born on the same day.
f) a has the same first name as b.
I have the knowledge about the reflexive, symmetric, anti-symmetric, and transitive also I can able to solve the problems when the relations are defined in ordered pairs. But can't able to visualize this kind of relations.
a) is reflexive because everyone who has visited web page $a$ has also visited web page $a$. It is not symmetric because if everyone who has visited web page $a$ has visited web page $b$, this does not mean that everyone who has visited web page $b$ has also visited web page $a$. It is also not antisymmetric, because if everyone who has visited web page $a$ has visited web page $b$ and everyone has visited web page $b$ has visited web page $a$, it does not necessarily mean that $a$ and $b$ are the same web page. It is transitive because if everyone who has visited web page $a$ also has visited web page $b$ and everyone who has visited web page $b$ also has visited web page $c$, then it follows that everyone who has visited web page $a$ has also visited web page $c$.
b) is not transitive because even though there are no common links found on web page $a$ and web page $b$ and there are no common links found on web page $b$ and web page $c$, there may still be common links found on web page $a$ and $c$.
d) is not reflexive, because $a$ can not be taller than itself.
f) is symmetric, because if $a$ has the same first name as $b$, then $b$ also has the same first name as $a$.
I will leave the rest to you.