MySQL joining 2 tables in to one main table - mysql

Question

I have 2 tables 'cat' and 'sub_cat' and these two tables should join or something with main table 'product'
I tried all joining methods and non of them gave me right result I want.
I'm sure there is a method. I don't know what to call.
Sample SQL
This is how the last query should be
forget about the normalization theories and every thing and I just want the last query to be like this or mysql method that I can use on this.
cat_id cannot be duplicate
s_id should also cannot be duplicate
like in third row there can be: cat_id but no s_id the s_id should be null
if there is no cat_id and no s_id both should be null like fourth row
p_id can be duplicate
can't use group by or distinct cause it doesn't give null values then as i know
only method i got closer is using left joining both cat and sub_cat to prod table but it gives me duplicate cat_id and s_id and can't use group by or distinct on this cause there should be null values.
here is the test data
CREATE TABLE IF NOT EXISTS `cat` (
`product_id` int(11) DEFAULT NULL,
`cat_id` int(11) DEFAULT NULL,
`cat_name` varchar(10) DEFAULT NULL
) ENGINE=MyISAM DEFAULT CHARSET=utf8;
INSERT INTO `cat` (`product_id`, `cat_id`, `cat_name`) VALUES
(1, 1, 'cat1'),
(2, 2, 'cat2'),
(3, 3, 'cat3'),
(1, 4, 'ca4');
CREATE TABLE IF NOT EXISTS `prod` (
`product_id` int(11) DEFAULT NULL,
`name` varchar(10) DEFAULT NULL
) ENGINE=MyISAM DEFAULT CHARSET=utf8;
INSERT INTO `prod` (`product_id`, `name`) VALUES
(1, 'prod1'),
(2, 'prod2'),
(3, 'pro3'),
(4, 'prod4');
CREATE TABLE IF NOT EXISTS `sub_cat` (
`product_id` int(11) DEFAULT NULL,
`sub_cat_id` int(11) DEFAULT NULL,
`sub_cat_name` varchar(10) DEFAULT NULL
) ENGINE=MyISAM DEFAULT CHARSET=utf8;
INSERT INTO `sub_cat` (`product_id`, `sub_cat_id`, `sub_cat_name`) VALUES
(1, 1, 'sub cat 1'),
(2, 2, 'sub cat 2'),
(1, 3, 'sub3');

Answer 1

I have done a similar thing in this one.prop_cat acts as you Category table,prop_subcat as your subcategory table and property as you product.
CREATE TABLE `prop_cat` (
`pcat_id` int(11) NOT NULL AUTO_INCREMENT,
`pcat_name` varchar(60) DEFAULT NULL,
PRIMARY KEY (`pcat_id`)
) ENGINE=InnoDB AUTO_INCREMENT=5 DEFAULT CHARSET=utf8;
CREATE TABLE `prop_subcat` (
`psubcat_id` int(11) NOT NULL,
`pcat_id` int(11) NOT NULL,
`psubcat_name` varchar(45) DEFAULT NULL,
PRIMARY KEY (`psubcat_id`,`pcat_id`),
KEY `pspc_idx` (`pcat_id`),
CONSTRAINT `catsub` FOREIGN KEY (`pcat_id`) REFERENCES `prop_cat` (`pcat_id`) ON DELETE NO ACTION ON UPDATE NO ACTION
) ENGINE=InnoDB DEFAULT CHARSET=utf8;
CREATE TABLE `property` (
`prop_id` int(11) NOT NULL AUTO_INCREMENT,
`prop_name` varchar(25) DEFAULT NULL,
`price` double DEFAULT NULL,
`location` varchar(50) DEFAULT NULL,
`image` varchar(60) DEFAULT NULL,
`area` double DEFAULT NULL,
`psubcat_id` int(11) DEFAULT NULL,
`description` text,
PRIMARY KEY (`prop_id`),
KEY `psub_idx` (`psubcat_id`),
CONSTRAINT `psub` FOREIGN KEY (`psubcat_id`) REFERENCES `prop_subcat` (`pcat_id`) ON DELETE NO ACTION ON UPDATE NO ACTION
) ENGINE=InnoDB AUTO_INCREMENT=6 DEFAULT CHARSET=utf8;
SELECT
prop_cat.`pcat_id` AS prop_cat_pcat_id,
prop_cat.`pcat_name` AS prop_cat_pcat_name,
prop_subcat.`psubcat_id` AS prop_subcat_psubcat_id,
prop_subcat.`pcat_id` AS prop_subcat_pcat_id,
prop_subcat.`psubcat_name` AS prop_subcat_psubcat_name,
property.`prop_id` AS property_prop_id,
property.`prop_name` AS property_prop_name,
property.`price` AS property_price,
property.`location` AS property_location,
property.`image` AS property_image,
property.`area` AS property_area,
property.`psubcat_id` AS property_psubcat_id,
property.`description` AS property_description
FROM
`prop_cat` prop_cat INNER JOIN `prop_subcat` prop_subcat ON prop_cat.`pcat_id` = prop_subcat.`pcat_id`
INNER JOIN `property` property ON prop_subcat.`pcat_id` = property.`psubcat_id`