jQuery AJAX请求只发送第一个表单，忽略其他表单

I am trying to create a table of products where a user can add and delete items to their basket. I am writing the basket content to a 'temp' table in my DB. I originally just had this executing via PHP but didn't like the redirecting so I toyed with using jQuery and a separate PHP file to make things act a lot cleaner and smoother.

Now when I tried this with a single product row it worked fine. So I then tried it with two and three rows. When I do this the it works correctly for the first row however, when I try it with the second or third rows it redirects to the action page and I don't understand why. It does write to the database perfectly fine.

Here is the code for the products page

<table class="table table-condensed">
    <tr>
        <td>
            <form id="addItem" action="addBasket.php" method="post">
            <input type="hidden" name="product" value="3">
            <button id="add" class="btn btn-link"><i class="fa fa-plus-square-o"></i></button>
            </form>
        </td>
        <td>
            <form id="remItem" action="remBasket.php" method="post">
            <input type="hidden" name="product" value="3">
            <button id="rem" class="btn btn-link"><i class="fa fa-minus-square-o"></i></button>
            </form>
        </td>
        <td>
            <form id="remAll" action="allBasket.php" method="post">
            <input type="hidden" name="product" value="3">
            <button id="all" class="btn btn-link"><i class="fa fa-trash"></i></button>
            </form>
        </td>
    </tr>
    <tr>
        <td>
            <form id="addItem" action="addBasket.php" method="post">
            <input type="hidden" name="product" value="4">
            <button id="add" class="btn btn-link"><i class="fa fa-plus-square-o"></i></button>
            </form>
        </td>
        <td>
            <form id="remItem" action="remBasket.php" method="post">
            <input type="hidden" name="product" value="4">
            <button id="rem" class="btn btn-link"><i class="fa fa-minus-square-o"></i></button>
            </form>
        </td>
        <td>
            <form id="remAll" action="allBasket.php" method="post">
            <input type="hidden" name="product" value="4">
            <button id="all" class="btn btn-link"><i class="fa fa-trash"></i></button>
            </form>
        </td>
    </tr>
</table>

This is then actioned by the following Javascript:

$("#add").click( function() {


$.post( $("#addItem").attr("action"),
         $("#addItem :input").serializeArray(),
         function(info){ $("#result").html(info);
   });
});

$("#addItem").submit( function() {
  return false;
});
$("#rem").click( function() {
 $.post( $("#remItem").attr("action"),
         $("#remItem :input").serializeArray(),
         function(info){ $("#result").html(info);
   });
});

$("#remItem").submit( function() {
  return false;
});
$("#all").click( function() {
 $.post( $("#remAll").attr("action"),
         $("#remAll :input").serializeArray(),
         function(info){ $("#result").html(info);
   });
});

$("#remAll").submit( function() {
  return false;
});

And I would post all three addBasket.php, remBasket.php, allBasket.php but you'll get the jist from just the addBasket file, if I need to post all three please let me know:

    require_once 'core/init.php';
$token = Session::get('user_session');
$product = $_POST['product'];

$exists = DB::getInstance()->query("SELECT * FROM temp WHERE token='$token' AND product='$product'");
    if($exists->count()){
        $qty = $exists->first()->qty + 1;
        DB::getInstance()->query("UPDATE temp SET qty='$qty' WHERE token='$token' AND product='$product'");
    }else{
        DB::getInstance()->insert('temp', array(
            'token' => $token,
            'product' => $product,
            'qty' => 1
            ));
    }

I will be using much more than two or three rows, the product table will be pulled from a products table and my hope was to use the products id as the value of the hidden field for each row.

What I would like to know primarily is how to stop the redirect happening, if anyone can suggest a neater or more efficient method for this it would be greatly appreciated.

Many thanks

Dave