Edit in JSFiddle

$('#attr').on('click', function() {
    var checked = $('#checkbox').is(':checked');
    $('#checkbox').attr('checked', !checked);
});

$('#prop').on('click', function() {
    var checked = $('#checkbox').is(':checked');
    $('#checkbox').prop('checked', !checked);
});

<div>
    <input id="checkbox" type="checkbox">
    <button id="attr">attr</button>
        <button id="prop">prop</button>
</div>