// Check
document.getElementById("checkbox").checked = true;

// Uncheck
document.getElementById("checkbox").checked = false;

// Check
$("#checkbox").prop("checked", true);

// Uncheck
$("#checkbox").prop("checked", false);

// Check
$("#checkbox").attr("checked", true);

// Uncheck
$("#checkbox").attr("checked", false);

document.getElementById('checkbox').click();

function toggle(checked) {
  var elm = document.getElementById('checkbox');
  if (checked != elm.checked) {
    elm.click();
  }
}

document.getElementById("id-of-checkbox").checked = true;

document.getElementById("id-of-checkbox").checked = false;

$('id of the checkbox')[0].checked = true

$('id of the checkbox')[0].checked = false

//Check
document.getElementById('checkbox').setAttribute('checked', 'checked');

//UnCheck
document.getElementById('chk').removeAttribute('checked');

<script type="text/javascript">
    $(document).ready(function () {
        $('.selecctall').click(function (event) {
            if (this.checked) {
                $('.checkbox1').each(function () {
                    this.checked = true;
                });
            } else {
                $('.checkbox1').each(function () {
                    this.checked = false;
                });
            }
        });

    });

</script>

function setCheckboxValue(checkbox,value) {
    if (checkbox.checked!=value)
        checkbox.click();
}