Return events that take place on date based on list of events with date ranges

For part 1 of the problem I figured out the following solution:

=ArrayFormula(index('Form responses '!$A:$A,small(if(('Form responses '!$C:$C<=$A2)*('Form responses '!$D:$D>=$A2),row('Form responses '!$A:$A)-row(index('Form responses '!$A:$A,1,1))+1),1)))

Anyone have an idea on how to add the "only on days" part of the problem?