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:
|   SalesOrderID |   SalesOrderDetailID |   OrderQty |   ProductID |   UnitPriceDiscount | Color_many   | Name                           | ProductNumber   | Color   |
|---------------:|---------------------:|-----------:|------------:|--------------------:|:-------------|:-------------------------------|:----------------|:--------|
|          53390 |                46594 |          1 |         979 |                   0 | Blue         | Touring-3000 Blue, 50          | BK-T18U-50      | Blue    |
|          63523 |                84373 |          1 |         867 |                   0 | Black        | Women's Mountain Shorts, S     | SH-W890-S       | Black   |
|          70027 |               106195 |          1 |         714 |                   0 | Multi        | Long-Sleeve Logo Jersey, M     | LJ-0192-M       | Multi   |
|          64968 |                87966 |          1 |         922 |                   0 | None         | Road Tire Tube                 | TT-R982         | None    |
|          49860 |                29973 |          2 |         823 |                   0 | Black        | LL Mountain Rear Wheel         | RW-M423         | Black   |
|          73371 |               117138 |          1 |         923 |                   0 | None         | Touring Tire Tube              | TT-T092         | None    |
|          66729 |                94005 |          1 |         929 |                   0 | None         | ML Mountain Tire               | TI-M602         | None    |
|          55294 |                55594 |          4 |         999 |                   0 | Black        | Road-750 Black, 52             | BK-R19B-52      | Black   |
|          59986 |                72780 |          1 |         870 |                   0 | None         | Water Bottle - 30 oz.          | WB-H098         | None    |
|          51832 |                42074 |         14 |         867 |                   0 | Black        | Women's Mountain Shorts, S     | SH-W890-S       | Black   |
|          43864 |                  680 |          1 |         748 |                   0 | Silver       | HL Mountain Frame - Silver, 38 | FR-M94S-38      | Silver  |
|          72506 |               114956 |          1 |         976 |                   0 | Yellow       | Road-350-W Yellow, 48          | BK-R79Y-48      | Yellow  |
|          72616 |               115246 |          1 |         871 |                   0 | None         | Mountain Bottle Cage           | BC-M005         | None    |
|          51690 |                39160 |          3 |         867 |                   0 | Black        | Women's Mountain Shorts, S     | SH-W890-S       | Black   |
|          74135 |               119075 |          1 |         708 |                   0 | Black        | Sport-100 Helmet, Black        | HL-U509         | Black   |
|          55270 |                55257 |          7 |         712 |                   0 | Multi        | AWC Logo Cap                   | CA-1098         | Multi   |
|          60487 |                74021 |          1 |         922 |                   0 | None         | Road Tire Tube                 | TT-R982         | None    |
|          65095 |                88281 |          1 |         974 |                   0 | Yellow       | Road-350-W Yellow, 42          | BK-R79Y-42      | Yellow  |
|          46344 |                 9896 |          1 |         754 |                   0 | Red          | Road-450 Red, 58               | BK-R68R-58      | Red     |
|          49068 |                26035 |          7 |         760 |                   0 | Red          | Road-650 Red, 60               | BK-R50R-60      | Red     |
|          69466 |               103596 |          2 |         998 |                   0 | Black        | Road-750 Black, 48             | BK-R19B-48      | Black   |
|          72656 |               115362 |          1 |         870 |                   0 | None         | Water Bottle - 30 oz.          | WB-H098         | None    |
|          44319 |                 2675 |          1 |         748 |                   0 | Silver       | HL Mountain Frame - Silver, 38 | FR-M94S-38      | Silver  |
|          53472 |                47366 |         11 |         858 |                   0 | Black        | Half-Finger Gloves, S          | GL-H102-S       | Black   |
|          71803 |               111261 |          2 |         868 |                   0 | Black        | Women's Mountain Shorts, M     | SH-W890-M       | Black   |
|          68624 |               100290 |          1 |         708 |                   0 | Black        | Sport-100 Helmet, Black        | HL-U509         | Black   |
|          54087 |                51609 |          1 |         870 |                   0 | None         | Water Bottle - 30 oz.          | WB-H098         | None    |
|          66921 |                94490 |          1 |         873 |                   0 | None         | Patch Kit/8 Patches            | PK-7098         | None    |
|          45813 |                 8068 |          8 |         765 |                   0 | Black        | Road-650 Black, 58             | BK-R50B-58      | Black   |
|          63763 |                84969 |          1 |         711 |                   0 | Blue         | Sport-100 Helmet, Blue         | HL-U509-B       | Blue    |
|          57154 |                62850 |          6 |         870 |                   0 | None         | Water Bottle - 30 oz.          | WB-H098         | None    |
|          71764 |               110541 |          1 |         872 |                   0 | None         | Road Bottle Cage               | BC-R205         | None    |
|          65154 |                88430 |         10 |         869 |                   0 | Black        | Women's Mountain Shorts, L     | SH-W890-L       | Black   |
|          53788 |                50888 |          1 |         860 |                   0 | Black        | Half-Finger Gloves, L          | GL-H102-L       | Black   |
|          58997 |                69388 |          7 |         715 |                   0 | Multi        | Long-Sleeve Logo Jersey, L     | LJ-0192-L       | Multi   |
|          51090 |                35782 |          3 |         907 |                   0 | Silver       | Rear Brakes                    | RB-9231         | Silver  |
|          67079 |                94865 |          1 |         797 |                   0 | Yellow       | Road-550-W Yellow, 38          | BK-R64Y-38      | Yellow  |
|          47721 |                19500 |          4 |         768 |                   0 | Black        | Road-650 Black, 44             | BK-R50B-44      | Black   |
|          60614 |                74335 |          1 |         880 |                   0 | Silver       | Hydration Pack - 70 oz.        | HY-1023-70      | Silver  |
|          48380 |                23841 |          2 |         825 |                   0 | Black        | HL Mountain Rear Wheel         | RW-M928         | Black   |
|          50297 |                32710 |          5 |         764 |                   0 | Red          | Road-650 Red, 52               | BK-R50R-52      | Red     |
|          48363 |                23605 |          2 |         761 |                   0 | Red          | Road-650 Red, 62               | BK-R50R-62      | Red     |
|          51776 |                41067 |          2 |         708 |                   0 | Black        | Sport-100 Helmet, Black        | HL-U509         | Black   |
|          53091 |                45856 |          1 |         922 |                   0 | None         | Road Tire Tube                 | TT-R982         | None    |
|          62318 |                79702 |          1 |         928 |                   0 | None         | LL Mountain Tire               | TI-M267         | None    |
|          49837 |                29580 |          1 |         767 |                   0 | Black        | Road-650 Black, 62             | BK-R50B-62      | Black   |
|          63180 |                82455 |          2 |         801 |                   0 | Yellow       | Road-550-W Yellow, 48          | BK-R64Y-48      | Yellow  |
|          53170 |                46048 |          1 |         784 |                   0 | Black        | Mountain-200 Black, 46         | BK-M68B-46      | Black   |
|          69557 |               104879 |          4 |         869 |                   0 | Black        | Women's Mountain Shorts, L     | SH-W890-L       | Black   |
|          73724 |               118047 |          1 |         712 |                   0 | Multi        | AWC Logo Cap                   | CA-1098         | Multi   |



label: ProductID
Name
ProductID
ProductNumber
ProductID
Color
output: {"Functional-Dependency": [["ProductID", "Name"], ["ProductID", "ProductNumber"], ["ProductID", "Color"]]}
labeled_fds: ProductID
Name
ProductID
ProductNumber
ProductID
Color
SalesOrderID
Name
source: $MMTU_HOME/resources/Relationship-finding/FD/100072050