How to enable a disabled checkbox dynamically?

Just do

function enable() {
    document.getElementById("check").disabled= false;

}

function disable() {
     document.getElementById("check").disabled= true;
}

With this you are setting the property of the DOM element, while setting attribute presence of attribute disabled will disable the check box, so even if you do x.setAttribute("disabled", "false"); it will still be there on the element as attribute.

Demo

or you would just do:

function disable() {
    document.getElementById("check").setAttribute('disabled', 'disabled');
}

function enable() {
   document.getElementById("check").removeAttribute('disabled');
}

disabled as attribute and disabled as property are different.