How do I validate a text entry choice for a multiple choice, multiple answer question?

I have a multiple choice question that asks users to select all of the applications they have used from a list. I have an "other" option, with a text entry for them to fill out the name of the other application that was not listed. Right now my validation forces them to write in the text box if they have only selected "other". If they select multiple, e.g., "application 1 and other" they are not forced to enter in the text box.

My validation looks like this:

If: Other is selected - and - other text entry - is not empty,
OR
option a is selected
or option b is selected ...

etc.

How would I write the logic to force them to write in the text box as long as they have selected it?