This is pretty straight forward. Add a click handler to your div and update the value of your input using the val () method.
You did not post your markup, so I used some placeholder identifiers. You will need to update them for selectors working in your context:
Working demo
$('#myDiv').on('click', function() { var hiddenField = $('#myHiddenField'), val = hiddenField.val(); hiddenField.val(val === "true" ? "false" : "true"); });
Note that input values are always strings, so they will not be true Boolean.
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