I find these problems easy when it has to do with numbers, but I'm having trouble visualizing word problems.
The first question:
"Everyone who has visited web page a has also visited web page b".
The answer is Reflexive and Transitive. But I'm having trouble visualizing why.
So let's say the webpages are {Google, Yahoo, Bing, YouTube}
So when I list it out would like (Google, Google), (Yahoo, Yahoo), etc
Where (a, b) is person a and person b
I don't understand if (webpage a, webpage b) correlates to person a person b is my question. Could someone help explain this overall problem?
It might help to realize that the relation is actually the subset relation on a certain family of sets. For each web page $w$ let $P(w)$ be the set of people who have visited $w$. If $R$ is the relation in question, then $\langle w_1,w_2\rangle\in R$ if and only if $P(w_1)\subseteq P(w_2)$: the set of people who have visited $w_1$ is a subset of the set of people who have visited $w_2$. Since $\subseteq$ is reflexive and transitive, $R$ should be as well, but we can verify this in detail.
Clearly $P(w)\subseteq P(w)$ for every web page $w$, so $\langle w,w\rangle\in R$ for each web page $w$, and $R$ is therefore reflexive.
If $\langle w_1,w_2\rangle\in R$ and $\langle w_2,w_3\rangle\in R$, then $P(w_1)\subseteq P(w_2)$, and $P(w_2)\subseteq P(w_3)$, so $P(w_1)\subseteq P(w_3)$. But that means that $\langle w_1,w_3\rangle\in R$ and hence that $R$ is transitive.