I have just started to learn Topology, using specifically the book mentioned in the title. I have placed that information in the title with SEO in mind, if this is not acceptable practice in this community, please re/move it as necessary. I have studied the required MATHJAX and LATEX, and have hopefully written it to a satisfactory level. The questions are listed and my attempts or logic accompany them
If $X=\{a,b,c,d,e,f\}$ and $\tau$ is the discrete topology on $X$, which of the following statements are true?
$a) X\in\tau$: True - Required to be considered a topology.
$b) \{X\}\in\tau$: False - We have the set $a)$, but this is a set within a set.
$c) \{\emptyset\}\in\tau$: False - As above, but in regards to $\emptyset$
$d) \emptyset\in\tau$: True
$e) \emptyset \in X$: True of all sets
$f) \{\emptyset\}\in X$: False as of $c)$
$g) \{a\}\in\tau$: True since $\{a\}\subseteq X$ and the discrete topology takes all possible subsets.
$h) a \in \tau$: False $a$ would need to be a subset. See $n)$.
$i) \emptyset \subseteq X$: True, it is a subset
$j) \{a\}\in X$: False, true of $g)$, but here $a$ would need to be an element to be within $X$
$k) \{\emptyset \} \subseteq X$: False this is a set in a set.
$l) a \in X$: True
$m) X \subseteq \tau$: True
$n) \{a\}\subseteq \tau$: True, since this is a set within $\tau$
$o) \{X\}\subseteq \tau$: False, this is a set in a set.
$p) a \subseteq \tau$: False, this is an element and not a set.
Sorry for the large text wall. Please leave me a comment in regards to things I should avoid doing in my question, and/or any preferable formatting action I can complete. Thank you for your time.