Below JavaScript code snippet explains how to change the state of HTML input checkbox to check and uncheck using jQuery
<input type="checkbox" id="Checkbox1" value = "1" />
<input type="button" id="check" value = "Check" />
<input type="button" id="uncheck" value = "Uncheck" />
 
<script type = "text/javascript" src = "http://ajax.aspnetcdn.com/ajax/jQuery/jquery-1.6.1.min.js"></script>
<script type="text/javascript">
    $("#check").live("click", function () {
        $("#Checkbox1").attr("checked", "checked");
    });
    $("#uncheck").live("click", function () {
        $("#Checkbox1").removeAttr("checked");
    });
</script>
 
 
Explanation:
In the above example a click event handler has been assigned to the two HTML input buttons with ids check and uncheck, when the check button is clicked, the checked  property of checkbox is set to checked and when the uncheck button is clicked the checked  property of the checkbox is removed using removeAttr method of jQuery.