Partial ordering set subset relation

Question

Hi I am a newbie with poset partial order sets, can anyone help with below.

If P consists of all subsets of {1,2,3,4}

How may edges does the cover graph of the poset P, C have?

C is the subset relation A C B

If A is a subset of B

I know I have to show a hasse diagram and I believe a subset relation chart will be same as less than equal, but unsure can someone explain.

Thanks

Answer 1

Hint:

There is a one-to-one relation between functions $f:X\to\{1,2,3\}$ and pairs $(A,B)$ with $A,B\subseteq X$ and $A\subseteq B$.

This by setting $A=\{i\mid f(i)=1\}$ and $B=\{i\mid f(i)\in\{1,2\}\}$.