** Using WeBWorK **

Use

Context()->strings->add(
  "null set" => {TeX => "\varnothing"}
);

to set the TeX version of the string to \varnothing.

If you use this for student answers, you may run into some troubles.

For example, you should be sure to add the typeMatch option when you use this as a correct answer so that you can get correct error messages:

ANS(Compute("null set")->cmp(typeMatch=>Value::Set));

(otherwise the error messages will say they are looking for a number not a set).

Also, if a student answers {} or some set expression that leads to an empty set, e.g., [1,2]-(0,3), then their answer will be marked wrong.

On the other hand, you might be better off with a constant rather than a string object for this (since the null set is already something that has a MathObject that can represent it). The only problem is that constants normally aren't allowed to have spaces in their names, so you have to fix the allowed name pattern as well:

Context("Interval");
Context()->{_constants}{namePattern} = qr/[a-zA-Z][a-zA-Z0-9_ ]*/;  # allow space in constant names
Context()->update;

Context()->constants->add(
  "null set" => Set(),     # the empty set
);

or

Context("Interval");
Context()->{_constants}{namePattern} = qr/[a-zA-Z][a-zA-Z0-9_ ]*/;  # allow space in constant names
Context()->update;

Context()->constants->add(
  "null set" => {value => Set(), TeX => "\varnothing"}
);

if you really want this to show up as the symbol. I'm not sure I'd do that, however. If you use "null set" as the correct answer, then the correct answer column will show the symbol, and it will not be clear to the students how to enter the answer (unless they use the hover tooltip to see what to type). Also, if they enter null sets in other ways, like as {}, which is the default means of doing it, then it will not show up as the empty-set symbol.