Task: Functional-Dependency (source dataset: Auto-Relate)

Given a table represented shown below, your task is to determine functional dependencies that exist in the table. Recall that a functional dependency is a relationship where the value of one attribute (or a set of attributes), known as the determinant columns, can uniquely determines the value of another attribute, known as the dependent columns (e.g., student-ID => student-Name, car-model => car-make, employee-ID => department, etc.).

Instructions:
Analyze the provided table below, identify all functional dependencies that should semantically hold in the table. Do not produce spurious relationships that not semantically meaningful.

No explanation, format the output as a JSON object:{"Functional-Dependency": <list of functional dependencies>}. Each functional dependency should be represented as [<determinant column>, <dependent column>]

Input Table:
| transaction_date        | stock_date   |   product_id |   customer_id |   store_id |   quantity | product_brand   | product_name                         |   product_sku |   product_retail_price |   product_cost |   product_weight |
|:------------------------|:-------------|-------------:|--------------:|-----------:|-----------:|:----------------|:-------------------------------------|--------------:|-----------------------:|---------------:|-----------------:|
| 1998-01-05 00:00:00.000 | 4/24/1998    |          162 |           128 |         13 |          4 | Denny           | Denny Large Sponge                   |   18693817257 |                    285 |            123 |              138 |
|                         | 6/18/1998    |         1009 |         10031 |         24 |          4 | American        | American Roasted Chicken             |   81011092066 |                    297 |            116 |              123 |
|                         | 1/12/1998    |          284 |          4010 |         11 |          2 | Super           | Super Chunky Peanut Butter           |   32421942353 |                     99 |             49 |              771 |
|                         | 6/27/1997    |          377 |          2969 |          6 |          3 | Moms            | Moms Low Fat Bologna                 |   24599472880 |                     21 |             71 |               18 |
|                         | 1/24/1998    |          901 |          7261 |         12 |          4 | Fantastic       | Fantastic Pumpernickel Bread         |   52551395297 |                    299 |            141 |              135 |
|                         | 4/15/1998    |          929 |          9416 |         19 |          3 | BBB Best        | BBB Best Oregano                     |   54031245112 |                     53 |              2 |              128 |
| 1998-06-11 00:00:00.000 | 11/3/1998    |         1390 |          4879 |         24 |          3 | Sunset          | Sunset 75 Watt Lightbulb             |   40330317616 |                    191 |             88 |              187 |
|                         | 11/17/1997   |          620 |          9715 |         17 |          4 | Landslide       | Landslide Extra Chunky Peanut Butter |   98511744141 |                     73 |             28 |               78 |
|                         | 9/13/1998    |           72 |          4066 |          3 |          5 | Red Spade       | Red Spade Corned Beef                |   36696267724 |                    274 |            101 |              202 |
|                         | 6/16/1998    |          102 |          1504 |         24 |          3 | Golden          | Golden Lime Popsicles                |   55682595372 |                    245 |             81 |              182 |
|                         | 1/24/1998    |         1488 |          8116 |         13 |          2 | Fort West       | Fort West Chocolate Donuts           |   26275478005 |                    234 |             94 |              122 |
|                         | 8/20/1998    |         1516 |          3982 |          8 |          4 | Top Measure     | Top Measure Light Wine               |   78401270508 |                    336 |            165 |               10 |
| 1998-02-07 00:00:00.000 | 6/30/1998    |         1217 |          7961 |          2 |          1 | Sphinx          | Sphinx Muffins                       |   34239718317 |                    127 |             61 |              181 |
| 1997-08-05 00:00:00.000 | 5/3/1997     |          347 |          5123 |         11 |          4 | Better          | Better Fancy Canned Sardines         |   16011533141 |                     12 |             44 |              118 |
| 1997-03-10 00:00:00.000 | 9/28/1997    |         1405 |          7565 |         15 |          4 | Sunset          | Sunset Copper Cleaner                |   63254396319 |                     89 |             33 |              172 |
|                         | 9/16/1998    |          569 |          3009 |          6 |          3 | Atomic          | Atomic Spicy Mints                   |   18916108012 |                    316 |            158 |              779 |
|                         | 10/24/1998   |            6 |          2896 |          3 |          3 | Washington      | Washington Cola                      |   29804642796 |                    115 |             37 |              158 |
| 1998-07-12 00:00:00.000 | 12/5/1998    |          267 |          1693 |         12 |          4 | Good            | Good Light Wine                      |   79031686186 |                     83 |             28 |              698 |
| 1997-11-03 00:00:00.000 | 3/4/1997     |         1209 |          9548 |         15 |          3 | Portsmouth      | Portsmouth Chardonnay                |   51954743266 |                     27 |             84 |              131 |
| 1997-05-12 00:00:00.000 | 12/3/1997    |          922 |          6201 |         15 |          3 | BBB Best        | BBB Best Grape Preserves             |   68103712201 |                    259 |             88 |              132 |
| 1998-04-01 00:00:00.000 | 12/30/1997   |         1155 |          5256 |         17 |          2 | Horatio         | Horatio Low Fat Cookies              |   11329383254 |                    188 |             81 |              161 |
| 1997-09-09 00:00:00.000 | 9/6/1997     |         1114 |          6899 |          7 |          4 | Tri-State       | Tri-State Beets                      |   33651273846 |                    342 |             12 |              206 |
|                         | 12/23/1998   |         1411 |          9116 |         12 |          4 | Sunset          | Sunset Large Sponge                  |   73550452589 |                     19 |             59 |              174 |
| 1998-05-11 00:00:00.000 | 11/4/1998    |          805 |          5301 |          6 |          4 | Ebony           | Ebony Red Pepper                     |   61792613863 |                    288 |            112 |              169 |
|                         | 9/13/1998    |          284 |          3125 |          8 |          5 | Super           | Super Chunky Peanut Butter           |   32421942353 |                     99 |             49 |              771 |
| 1997-06-07 00:00:00.000 | 7/1/1997     |          629 |           440 |         15 |          4 | Token           | Token Diet Cola                      |   69160491824 |                     55 |             21 |               10 |
|                         | 12/14/1998   |          473 |          6944 |          1 |          3 | Red Wing        | Red Wing Large Sponge                |   82774483561 |                     73 |             27 |               14 |
| 1998-02-11 00:00:00.000 | 10/31/1998   |         1339 |          4392 |          6 |          3 | Carrington      | Carrington Waffles                   |   77714528441 |                    131 |              5 |              104 |
| 1998-12-03 00:00:00.000 | 3/9/1998     |          302 |          9819 |         12 |          3 | Super           | Super Oregano                        |   53702738881 |                    345 |            124 |              137 |
| 1998-07-10 00:00:00.000 | 10/5/1998    |         1306 |          9074 |         11 |          4 | Booker          | Booker Buttermilk                    |   16487196087 |                    247 |             86 |              131 |
|                         | 10/6/1997    |          933 |          9397 |         11 |          4 | BBB Best        | BBB Best Strawberry Jam              |   31341258883 |                    338 |            128 |              102 |
| 1998-02-10 00:00:00.000 | 9/29/1998    |          686 |           169 |         13 |          3 | Cutting Edge    | Cutting Edge Pimento Loaf            |   53289378285 |                    182 |             67 |              125 |
|                         | 12/12/1998   |         1545 |          2721 |         19 |          4 | CDR             | CDR Columbian Coffee                 |   25521809458 |                    229 |            112 |              952 |
| 1998-04-05 00:00:00.000 | 4/28/1998    |         1538 |          2467 |          1 |          2 | CDR             | CDR Decaf Coffee                     |   13621910214 |                     34 |            122 |              104 |
| 1998-02-03 00:00:00.000 | 2/24/1998    |          842 |          7075 |         15 |          2 | Nationeel       | Nationeel Low Fat BBQ Chips          |   42178552746 |                     32 |            138 |              189 |
|                         | 12/14/1998   |         1211 |          3192 |          1 |          2 | Portsmouth      | Portsmouth Light Beer                |   19633931517 |                    379 |            174 |              163 |
| 1998-05-06 00:00:00.000 | 6/1/1998     |          360 |          3911 |          6 |          4 | Carlson         | Carlson Low Fat String Cheese        |   10141282677 |                    131 |             51 |               98 |
| 1998-02-02 00:00:00.000 | 1/28/1998    |          708 |          5013 |          7 |          2 | Imagine         | Imagine Low Fat French Fries         |   26132355332 |                    368 |            151 |              979 |
| 1997-07-12 00:00:00.000 | 12/1/1997    |          667 |          5590 |         17 |          4 | Gorilla         | Gorilla Sour Cream                   |   90842847228 |                    266 |            101 |              212 |
|                         | 8/11/1997    |         1205 |          5707 |         23 |          2 | Portsmouth      | Portsmouth Light Wine                |   88120834231 |                     26 |            107 |              193 |
| 1997-07-03 00:00:00.000 | 2/28/1997    |         1490 |          7683 |         22 |          2 | Fort West       | Fort West Sesame Crackers            |   24716899991 |                     14 |             66 |              914 |
| 1998-10-09 00:00:00.000 | 9/3/1998     |          476 |          1025 |          9 |          4 | Quick           | Quick Seasoned Hamburger             |   82410421967 |                    364 |            113 |              156 |
|                         | 1/14/1998    |          733 |          3021 |         16 |          3 | Imagine         | Imagine Frozen Chicken Wings         |   89067804217 |                    195 |             94 |              166 |
|                         | 7/15/1997    |         1198 |           285 |          7 |          3 | Musial          | Musial White Chocolate Bar           |   58962443470 |                    343 |             13 |               16 |
| 1998-11-05 00:00:00.000 | 5/8/1998     |          323 |          5981 |         10 |          2 | Best            | Best Oatmeal                         |   75705832839 |                     35 |            123 |              154 |
|                         | 1/8/1998     |          538 |          5466 |          8 |          3 | Fast            | Fast Graham Crackers                 |   92419202923 |                     93 |             39 |              209 |
| 1998-07-12 00:00:00.000 | 11/30/1998   |          425 |          2338 |         15 |          3 | Steady          | Steady Tartar Control Toothpaste     |   26453244090 |                    128 |             42 |              918 |
|                         | 3/20/1998    |          179 |          5654 |          4 |          5 | High Top        | High Top Green Pepper                |   83242968916 |                    275 |             88 |              197 |
| 1997-06-09 00:00:00.000 | 9/5/1997     |          986 |          4194 |         24 |          3 | Even Better     | Even Better String Cheese            |   23160703778 |                     35 |             13 |              146 |
| 1998-07-01 00:00:00.000 | 1/2/1998     |         1533 |          7322 |         19 |          4 | CDR             | CDR Chunky Peanut Butter             |   31598665118 |                     25 |            103 |              763 |



label: product_id
product_brand
product_id
product_name
product_id
product_sku
product_id
product_retail_price
product_id
product_cost
product_id
product_weight
output: {"Functional-Dependency": [["product_id", "product_brand"], ["product_id", "product_name"], ["product_id", "product_sku"], ["product_id", "product_retail_price"], ["product_id", "product_cost"], ["product_id", "product_weight"]]}
labeled_fds: product_id
product_brand
product_id
product_name
product_id
product_sku
product_id
product_retail_price
product_id
product_cost
product_id
product_weight
customer_id
store_id
customer_id
product_sku
customer_id
product_cost
customer_id
product_weight
product_sku
store_id
product_retail_price
transaction_date
source: $MMTU_HOME/resources/Relationship-finding/FD/270213199