PHP processing - trolley1.php
<?php
session_start();
$product_ids = array();

    //check if Add to Cart button has been submitted
    if(filter_input(INPUT_POST, 'submit')){
    if(isset($_SESSION['cart'])){

    //keep track of how many products are in the cart
    $count = count($_SESSION['cart']);

    //create array for matching array keys to products id's
    $product_ids = array_column($_SESSION['cart'], 'id');

    if (!in_array(filter_input(INPUT_GET, 'id'), $product_ids)){
    $_SESSION['cart'][$count] = array(
        'id' => filter_input(INPUT_GET, 'id'),
         'name' => filter_input(INPUT_POST, 'name'),
         'price' => filter_input(INPUT_POST, 'price'),
         'quantity' => filter_input(INPUT_POST, 'quantity')
        );
    }
    else { //product already exists, increase quantity
        //match array key to id of the product being added to the cart
        for ($i = 0; $i < count($product_ids); $i++){
            if ($product_ids[$i] == filter_input(INPUT_GET, 'id')){
                //add item quantity to the existing product in the array
                $_SESSION['cart'][$i]['quantity'] += filter_input(INPUT_POST, 'quantity');
            }
        }
    }
}
    else { //if shopping cart doesn't exist, create first product with array key 0
    //create array using submitted form data, start from key 0 and fill it with values
    $_SESSION['cart'][0] = array(
        'id' => filter_input(INPUT_GET, 'id'),
        'name' => filter_input(INPUT_POST, 'name'),
        'price' => filter_input(INPUT_POST, 'price'),
        'quantity' => filter_input(INPUT_POST, 'quantity')
    );
  }
}

    cart.php
        <script>
    $(document).ready(function(){
    $('form[id=ajax]').submit(function(event){
    event.preventDefault();

    var formData = {
    submit: $('input[name=submit]').val(),
    id: $('input[name=id]').val(),
    name: $('input[name=name]').val(),
    price: $('input[name=price]').val(),
    quantity: $('input[name=quantity]').val()
    };

    $.ajax({
        type: 'POST',
        url: 'trolley1.php',
        data: formData,
        dataType: 'json',
       });
       });
       });
       </script>
<?php
echo "
  <div class='col-sm-3 mt-5'>
    <form id='ajax' method='post' action='trolley1.php?action=add&id=$id'>
      <div class='products'>
          <input id='form_id' type='hidden' name='id' value='$id' />
          <input id='form_name' type='hidden' name='name' value='$product' />
          <input id='form_price' type='hidden' name='price' value='$price' />
          <input id='form_quantity' type='text' name='quantity' class='form-control' value='1' />
          <input id='submit' type='submit' name='submit' style='margin-top:5px;' class='btn btn-info'
                 value='Add'/>
          <div id='get_content'></div>
      </div>
    </form>
  </div>