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:
| return_date             |   product_id |   store_id |   quantity | Product Brand   | product_name                        |   product_sku |   product_retail_price |   discount_price |   product_cost |   product_weight |   recyclable |   low_fat | price_tier   |
|:------------------------|-------------:|-----------:|-----------:|:----------------|:------------------------------------|--------------:|-----------------------:|-----------------:|---------------:|-----------------:|-------------:|----------:|:-------------|
| 1998-12-23 00:00:00.000 |           27 |         19 |          2 | Blue Label      | Blue Label Beef Soup                |   29712170958 |                   2.65 |             2.38 |           1.11 |            11.2  |            0 |         1 | Mid          |
| 1998-11-14 00:00:00.000 |          577 |          3 |          1 | Walrus          | Walrus Imported Beer                |   25103213191 |                   2.62 |             2.36 |           1.28 |             6.11 |            1 |         0 | Mid          |
| 1997-08-22 00:00:00.000 |         1231 |         17 |          1 | Plato           | Plato Tomato Sauce                  |   29154657721 |                   3.71 |             3.34 |           1.19 |            11.8  |            0 |         0 | High         |
| 1998-12-23 00:00:00.000 |         1322 |         11 |          2 | Lake            | Lake Sliced Turkey                  |   94018571972 |                   3.2  |             2.88 |           1.02 |             6.66 |            0 |         1 | High         |
| 1998-01-12 00:00:00.000 |          692 |          8 |          1 | Cutting Edge    | Cutting Edge Cole Slaw              |   37396603226 |                   1.55 |             1.4  |           0.56 |             6.19 |            1 |         1 | Mid          |
| 1998-11-01 00:00:00.000 |         1140 |         13 |          2 | Tri-State       | Tri-State Peaches                   |   64901562333 |                   2.56 |             2.3  |           1.08 |            10.5  |            0 |         1 | Mid          |
| 1998-07-03 00:00:00.000 |          958 |         13 |          1 | Just Right      | Just Right Canned Yams              |   37734969258 |                   1.36 |             1.22 |           0.57 |            19.7  |            1 |         0 | Mid          |
| 1998-08-10 00:00:00.000 |          681 |         23 |          1 | Gorilla         | Gorilla 1% Milk                     |   22163082957 |                   2.3  |             2.07 |           1.1  |             9.43 |            1 |         0 | Mid          |
| 1998-04-25 00:00:00.000 |          319 |          9 |          1 | Excellent       | Excellent Orange Juice              |   90040029883 |                   1.6  |             1.44 |           0.59 |             9.58 |            0 |         0 | Mid          |
| 1998-02-15 00:00:00.000 |          236 |          1 |          2 | Best Choice     | Best Choice Fondue Mix              |   98134089112 |                   1.81 |             1.63 |           0.67 |            10.8  |            0 |         1 | Mid          |
| 1998-05-25 00:00:00.000 |         1251 |         24 |          1 | Skinner         | Skinner Mango Drink                 |   92351836562 |                   3.58 |             3.22 |           1.47 |            11.4  |            1 |         0 | High         |
| 1998-01-19 00:00:00.000 |          469 |         12 |          1 | Red Wing        | Red Wing Silver Cleaner             |   87961875796 |                   1.29 |             1.16 |           0.58 |             8.03 |            1 |         0 | Mid          |
| 1998-11-28 00:00:00.000 |          179 |         11 |          1 | High Top        | High Top Green Pepper               |   83242968916 |                   2.75 |             2.48 |           0.88 |            19.7  |            0 |         1 | Mid          |
| 1998-10-07 00:00:00.000 |         1179 |         12 |          1 | Horatio         | Horatio Sesame Crackers             |   96515912413 |                   2.63 |             2.37 |           1.1  |            12.6  |            0 |         0 | Mid          |
| 1998-04-06 00:00:00.000 |          767 |         12 |          1 | Cormorant       | Cormorant 25 Watt Lightbulb         |   43628973364 |                   1.45 |             1.3  |           0.51 |            16.9  |            1 |         0 | Mid          |
| 1998-09-21 00:00:00.000 |          198 |         17 |          1 | High Top        | High Top Red Delcious Apples        |   78738434910 |                   0.92 |             0.83 |           0.31 |            17.2  |            1 |         1 | Low          |
| 1997-12-25 00:00:00.000 |           44 |         16 |          1 | Club            | Club Low Fat Sour Cream             |   50668345093 |                   2.93 |             2.64 |           1.08 |            10.7  |            0 |         1 | Mid          |
| 1997-12-03 00:00:00.000 |          936 |         15 |          1 | BBB Best        | BBB Best Extra Chunky Peanut Butter |   35550599694 |                   2.78 |             2.5  |           1.2  |             6.49 |            0 |         0 | Mid          |
| 1997-07-02 00:00:00.000 |         1375 |         16 |          1 | Hilltop         | Hilltop HCL Nasal Spray             |   75030302405 |                   2.13 |             1.92 |           0.77 |            21.1  |            1 |         0 | Mid          |
| 1998-03-08 00:00:00.000 |          112 |         19 |          1 | Golden          | Golden Lemon Popsicles              |   89050326943 |                   1.13 |             1.02 |           0.41 |             9.35 |            0 |         1 | Mid          |
| 1997-02-16 00:00:00.000 |         1414 |         24 |          1 | Gerolli         | Gerolli Seasoned Hamburger          |   13948624730 |                   1.34 |             1.21 |           0.66 |            19.5  |            1 |         0 | Mid          |
| 1998-12-20 00:00:00.000 |          565 |          7 |          1 | Atomic          | Atomic Mint Chocolate Bar           |   55082198977 |                   0.9  |             0.81 |           0.38 |            10.9  |            1 |         0 | Low          |
| 1998-08-08 00:00:00.000 |          312 |          3 |          2 | Excellent       | Excellent Berry Juice               |   20972600579 |                   2.13 |             1.92 |           0.66 |            12.6  |            1 |         0 | Mid          |
| 1997-07-10 00:00:00.000 |          962 |         23 |          1 | Just Right      | Just Right Regular Ramen Soup       |   61023109555 |                   1.87 |             1.68 |           0.79 |             9.31 |            1 |         1 | Mid          |
| 1998-06-11 00:00:00.000 |          836 |         16 |          1 | Ebony           | Ebony Party Nuts                    |   84476624131 |                   1.18 |             1.06 |           0.45 |            20.9  |            1 |         1 | Mid          |
| 1998-07-04 00:00:00.000 |         1506 |         12 |          1 | Gulf Coast      | Gulf Coast Bubble Gum               |   13452652096 |                   3.43 |             3.09 |           1.68 |            13.2  |            0 |         0 | High         |
| 1997-04-14 00:00:00.000 |          140 |          6 |          1 | Denny           | Denny Paper Cups                    |   53698855042 |                   1.82 |             1.64 |           0.8  |             6.03 |            0 |         0 | Mid          |
| 1997-11-26 00:00:00.000 |            7 |          6 |          1 | Washington      | Washington Diet Cola                |   20191444754 |                   2.61 |             2.35 |           0.91 |            18    |            1 |         0 | Mid          |
| 1997-12-25 00:00:00.000 |          911 |         17 |          2 | BBB Best        | BBB Best Chunky Peanut Butter       |   35828165411 |                   1.97 |             1.77 |           0.77 |             6.97 |            0 |         1 | Mid          |
| 1998-05-29 00:00:00.000 |          183 |         17 |          1 | High Top        | High Top Red Pepper                 |   80125812888 |                   2.41 |             2.17 |           1.04 |             7.06 |            1 |         0 | Mid          |
| 1997-12-14 00:00:00.000 |          453 |         23 |          2 | Red Wing        | Red Wing Toilet Bowl Cleaner        |   74269306063 |                   2.92 |             2.63 |           1.05 |            19.4  |            1 |         0 | Mid          |
| 1997-03-02 00:00:00.000 |         1220 |          7 |          2 | Sphinx          | Sphinx Wheat Bread                  |   66924591660 |                   1.95 |             1.76 |           0.94 |            10.1  |            1 |         1 | Mid          |
| 1998-07-19 00:00:00.000 |         1479 |         19 |          2 | Fort West       | Fort West No Salt Popcorn           |   49392418265 |                   1.46 |             1.31 |           0.61 |            18.3  |            1 |         1 | Mid          |
| 1998-07-11 00:00:00.000 |          271 |          3 |          1 | Good            | Good Chardonnay                     |   88599619269 |                   2.37 |             2.13 |           1.16 |            12    |            1 |         0 | Mid          |
| 1997-11-16 00:00:00.000 |         1482 |         11 |          1 | Fort West       | Fort West Avocado Dip               |   51315057873 |                   0.6  |             0.54 |           0.23 |            19.9  |            1 |         0 | Low          |
| 1998-08-03 00:00:00.000 |          261 |          8 |          1 | Medalist        | Medalist Ravioli                    |   57518588900 |                   3.38 |             3.04 |           1.42 |            17.5  |            1 |         0 | High         |
| 1998-04-26 00:00:00.000 |          282 |          6 |          2 | Great           | Great Wheat Bread                   |   95504987835 |                   0.93 |             0.84 |           0.36 |            13.6  |            1 |         0 | Low          |
| 1998-11-16 00:00:00.000 |          789 |         19 |          1 | Excel           | Excel Monthly Auto Magazine         |   50359107851 |                   3.62 |             3.26 |           1.74 |            19.7  |            1 |         0 | High         |
| 1998-01-28 00:00:00.000 |           61 |          9 |          1 | Club            | Club Strawberry Yogurt              |   93602067828 |                   0.74 |             0.67 |           0.37 |            13.4  |            0 |         1 | Low          |
| 1998-03-17 00:00:00.000 |         1099 |          8 |          1 | High Quality    | High Quality Scissors               |   94492883086 |                   3.24 |             2.92 |           1.33 |             9.42 |            1 |         0 | High         |
| 1998-09-22 00:00:00.000 |           25 |          8 |          1 | Blue Label      | Blue Label Chicken Noodle Soup      |   62032982707 |                   1.55 |             1.4  |           0.7  |             9.48 |            1 |         1 | Mid          |
| 1997-04-29 00:00:00.000 |         1210 |         15 |          1 | Portsmouth      | Portsmouth White Zinfandel Wine     |   90771597027 |                   1.7  |             1.53 |           0.83 |            11.2  |            1 |         0 | Mid          |
| 1998-03-29 00:00:00.000 |           11 |         12 |          1 | Washington      | Washington Apple Drink              |   17074288725 |                   3.51 |             3.16 |           1.65 |            20    |            0 |         1 | High         |
| 1998-11-12 00:00:00.000 |         1365 |         17 |          2 | Hilltop         | Hilltop Toothpaste                  |   45417320132 |                   0.53 |             0.48 |           0.24 |             6.18 |            1 |         0 | Low          |
| 1998-12-20 00:00:00.000 |          353 |          7 |          1 | Black Tie       | Black Tie City Map                  |   29412943720 |                   1.57 |             1.41 |           0.69 |             8.78 |            1 |         0 | Mid          |
| 1998-04-29 00:00:00.000 |         1511 |         11 |          1 | Jardon          | Jardon Manicotti                    |   49561676383 |                   1.2  |             1.08 |           0.44 |            11.5  |            1 |         1 | Mid          |
| 1997-02-03 00:00:00.000 |          684 |         15 |          1 | Gorilla         | Gorilla Blueberry Yogurt            |   21799021363 |                   0.68 |             0.61 |           0.22 |             9.71 |            1 |         1 | Low          |
| 1998-12-03 00:00:00.000 |          249 |         15 |          1 | Best Choice     | Best Choice Raisins                 |   32616745829 |                   1.59 |             1.43 |           0.68 |            20    |            0 |         0 | Mid          |
| 1997-09-20 00:00:00.000 |         1321 |         16 |          1 | Lake            | Lake Corned Beef                    |   55201718211 |                   2.49 |             2.24 |           1    |            16.9  |            1 |         0 | Mid          |
| 1998-06-11 00:00:00.000 |           21 |         16 |          1 | Blue Label      | Blue Label Vegetable Soup           |   43318244814 |                   2.33 |             2.1  |           0.89 |            19.7  |            0 |         1 | Mid          |



label: product_id
Product Brand
product_id
product_name
product_id
product_sku
product_id
product_retail_price
product_id
discount_price
product_id
product_cost
product_id
product_weight
product_id
recyclable
product_id
low_fat
product_id
price_tier
output: {"Functional-Dependency": [["product_id", "Product Brand"], ["product_id", "product_name"], ["product_id", "product_sku"], ["product_id", "product_retail_price"], ["product_id", "discount_price"], ["product_id", "product_cost"], ["product_id", "product_weight"], ["product_id", "recyclable"], ["product_id", "low_fat"], ["product_id", "price_tier"]]}
labeled_fds: product_id
Product Brand
product_id
product_name
product_id
product_sku
product_id
product_retail_price
product_id
discount_price
product_id
product_cost
product_id
product_weight
product_id
recyclable
product_id
low_fat
product_id
price_tier
product_id
quantity
product_name
quantity
source: $MMTU_HOME/resources/Relationship-finding/FD/174749645