Let $Y=\{\emptyset, \{\emptyset\}\}$ and let $\cup: Y\times Y\to Y$ be a binary operation.
a) Draw the following table in your answer book, then complete the table for the binary operation $\cup:Y\times Y\to Y$. (Note that $\cup$ is the existing set union operation. It is not an operation that you may arbitrarily define.)
$$\begin{array}{|c|c|c|} \hline \bigcup & \emptyset & \{\emptyset\} \\ \hline \emptyset \\ \hline \{\emptyset\} \\ \hline \end{array}$$
Please advise on the steps for answering a question like this.
So far, I assume that the first step would be to determine Y x Y.
Not sure how to proceed thereafter. Do I need to put something in list notation? Seems a bit too lengthy for 4 marks.
[The question is from a past exam of an introductory computer science module]
$\cup : Y\times Y\to Y$ means that: "$\cup$ is a function mapping arguments in $Y$ and $Y$ to a result in $Y$".
You're told that $\cup$ is the set union operator, and that $Y=\{\varnothing, \{\varnothing\}\}$
Thus you need simply fill out the table. For instance, $\varnothing \cup \varnothing = \varnothing$ so $\varnothing$ is what you put in the first row, first column entry.
Now complete the entries for $\;\varnothing\cup\{\varnothing\}\;$, $\;\{\varnothing\}\cup\varnothing\;$, and $\;\{\varnothing\}\cup\{\varnothing\}\;$
$$\begin{array}{|c|c|c|} \hline \cup & \emptyset & \{\emptyset\} \\ \hline \emptyset & \emptyset \\ \hline \{\emptyset\} \\ \hline \end{array}$$
So four empty boxes, four four marks. I've don't one, you do the rest.
That is all.