Let A be the set of strings of $0$’s and $1$’s of length $3$ or less. Define the relation of $d$ on $A$ by $xdy$ if $x$ is contained within $y$. For example, $01d101$.
a) Draw a digraph for this relation.
b) Do the same for the relation $p$ defined by $xpy$ if $x$ is a prefix of $y$. For example, $10p101$, but $01p101$ is false.
I don't understand what they are asking here, all I'm asking is to help simplify the question. I hope I haven't been to vague.
$A$ is a finite set. At first, you should find out all elements of A. Then find out all pairs $(a,a') \in A \times A$ that satisfy $ada'$.
Now you have to know what a digraph (= directed graph) is. If not, find out on wikipedia. All you have to do then is to write down the elements of $A$ and place the right arrows between the elements.