JS check if checkbox is checked keep initial value

Question

I have a form to update personal data with multiple checkboxes who can be initially checked or not.

<form method="post" id="up_mission">
    <input checked type="checkbox"  id="first">
    <input type="checkbox"  id="second">
    <button class="btn btn-default" type="submit" id="update_mission<?php echo $id_mission ?>"</button>
</form>

and the JS:

$(function() {
        $("form[id^='up_mission']").submit(function() {
         var value1 = document.getElementById("first").checked;
         var value2 = document.getElementById("second").checked;
         $.post("update_mission.php", {value1: value1, value2:value2}, functon(data) { console.log(data) });
    });
});

In update_mission.php there is a simple SQL query to update with news values and I also do var_dump($_POST); and the values printed for first and second are always the ones that I initially put in the <input> it doesn't matters if I uncheck or check the checkbox.

How can I fix it please?

Here is the part of the php file :

var_dump($_POST);
$first = $_POST['value1'];
$second = $_POST['value2'];
if ($first == "true") { $first = "on";}
else {$first = "0";}
if ($second == "true") { $second = "on";}
else {$second = "0";}
update_miss = "UPDATE table SET First = 'first', Second = 'second'[...] WHERE my_condition";
// I connect to my DB, and do the query, and there is no problem here
// I also have text input in my form and they update pretty well   

Answer 1

Use $('#first').is(':checked') and $('#second').is(':checked') to detect state of checkbox.

$(function() {
    $("form[id^='up_mission']").submit(function() {
     var value1 = $('#first').is(':checked') ? 1 : 0;
     var value2 = $('#second').is(':checked') ? 1 : 0;
     $.post("update_mission.php", {value1: value1, value2: value2}, functon(data) { console.log(data) });
});
});