a) Given a set $S$ with the $n$ elements, find the number of ordered pairs $(A,B)$ such that
i) $A \subseteq B \subseteq S$
ii) $A \subset B \subseteq S$
b) Let n be a positive integer and S a set of size n. How many relations $\approx$ on S are there that are:
i. an equivalence relation and a partial ordering?
ii. an equivalence relation and a total ordering?
Normally the topic that I ask about I have a general understanding of (Calculus) but I am having a really tough time with Discrete Maths... Any idea what I should do here?