Discrete Mathematics ordered pairs and equivalence relations

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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?