Set attribute with an empty string

I'm trying to toggle the required attribute on fields using jQuery. On page load I add the required attribute to the relevant elements:

$("[data-required]").attr("required", "");

Then I have a toggle function that does a number of things, including toggling the required attribute:

if ($(childInput).attr('data-required')) {
  if (element.checked) {
    $(childInput).attr('required', '');
    $(childInput).rules('add', { required: true });
  }
  if (!element.checked) {
    $(childInput).attr('required', false);
    $(childInput).rules('remove');
  }
}

However, in both cases (on page load and on toggle), the required attribute is being set to required="required". Am I using the incorrect syntax, or missing something here? I can't figure out why "required" would be inserted into the attribute value.

.attr("required", true); and .attr("required", "true"); are resulting in the same behaviour.

OK, I'm not entirely sure why, but this works:

$("[data-required]").prop("required", true);

The if statement in the toggle function:

if ($(childInput).attr('data-required')) {
  if (element.checked) {
    $(childInput).prop('required', true);
    $(childInput).rules('add', { required: true });
  }
  if (!element.checked) {
    $(childInput).attr('required', false);
    $(childInput).rules('remove');
  }
}