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:
|   Productcode |   Customercode |   Year Period Actual |   Year Period Actual_x |   Year Period Forecast |   Year Period Forecast0 |   Sales Last Year |   Sales Actual | Open Orders Actual_x   |   Sales & Open_x |   Foreacast proposal | Forecast Adjustments   | Comments   |   Total Forecast |   ProductCode | Product description   | Product code &      |   Subgroup code | Subgroup description   |   Group code | Group description   |   Family code | Family description   |
|--------------:|---------------:|---------------------:|-----------------------:|-----------------------:|------------------------:|------------------:|---------------:|:-----------------------|-----------------:|---------------------:|:-----------------------|:-----------|-----------------:|--------------:|:----------------------|:--------------------|----------------:|:-----------------------|-------------:|:--------------------|--------------:|:---------------------|
|        100001 |         200028 |               202108 |                  24260 |                 202211 |                   24275 |               210 |            214 |                        |              214 |                  220 |                        |            |              220 |        100001 | Product 1             | 100001 -Product 1   |            1100 | Subgroup 1             |          101 | Group 1             |             1 | Family 1             |
|        100001 |         200001 |               202108 |                  24260 |                 202110 |                   24262 |                90 |             92 | 22.0                   |              114 |                   94 |                        |            |              114 |        100001 | Product 1             | 100001 -Product 1   |            1100 | Subgroup 1             |          101 | Group 1             |             1 | Family 1             |
|        100101 |         200001 |               202108 |                  24260 |                 202110 |                   24262 |                90 |             92 | 22.0                   |              114 |                   94 |                        |            |              114 |        100101 | Product 101           | 100101 -Product 101 |            4700 | Subgroup 47            |          401 | Group 4             |             2 | Family 2             |
|        100076 |         200038 |               202108 |                  24260 |                 202210 |                   24274 |                90 |             92 |                        |               92 |                   94 |                        |            |               94 |        100076 | Product 76            | 100076 -Product 76  |            3800 | Subgroup 38            |          301 | Group 3             |             2 | Family 2             |
|        100093 |         200010 |               202108 |                  24260 |                 202210 |                   24274 |                90 |             92 |                        |               92 |                   94 |                        |            |               94 |        100093 | Product 93            | 100093 -Product 93  |            4400 | Subgroup 44            |          401 | Group 4             |             2 | Family 2             |
|        100094 |         200028 |               202108 |                  24260 |                 202209 |                   24273 |               110 |            112 |                        |              112 |                  116 |                        |            |              116 |        100094 | Product 94            | 100094 -Product 94  |            4400 | Subgroup 44            |          401 | Group 4             |             2 | Family 2             |
|        100095 |         200014 |               202108 |                  24260 |                 202206 |                   24270 |               367 |            375 |                        |              375 |                  386 |                        |            |              386 |        100095 | Product 95            | 100095 -Product 95  |            4500 | Subgroup 45            |          401 | Group 4             |             2 | Family 2             |
|        100084 |         200047 |               202108 |                  24260 |                 202202 |                   24266 |               314 |            321 | 79.0                   |              399 |                  330 |                        |            |              399 |        100084 | Product 84            | 100084 -Product 84  |            4100 | Subgroup 41            |          401 | Group 4             |             2 | Family 2             |
|        100076 |         200038 |               202108 |                  24260 |                 202201 |                   24265 |               150 |            153 | 38.0                   |              190 |                  158 |                        |            |              190 |        100076 | Product 76            | 100076 -Product 76  |            3800 | Subgroup 38            |          301 | Group 3             |             2 | Family 2             |
|        100094 |         200024 |               202108 |                  24260 |                 202110 |                   24262 |                90 |             92 | 22.0                   |              114 |                   94 |                        |            |              114 |        100094 | Product 94            | 100094 -Product 94  |            4400 | Subgroup 44            |          401 | Group 4             |             2 | Family 2             |
|        100095 |         200062 |               202108 |                  24260 |                 202203 |                   24267 |               489 |            498 | 122.0                  |              620 |                  513 |                        |            |              620 |        100095 | Product 95            | 100095 -Product 95  |            4500 | Subgroup 45            |          401 | Group 4             |             2 | Family 2             |
|        100094 |         200028 |               202108 |                  24260 |                 202210 |                   24274 |                90 |             92 |                        |               92 |                   94 |                        |            |               94 |        100094 | Product 94            | 100094 -Product 94  |            4400 | Subgroup 44            |          401 | Group 4             |             2 | Family 2             |
|        100094 |         200028 |               202108 |                  24260 |                 202201 |                   24265 |               150 |            153 | 38.0                   |              190 |                  158 |                        |            |              190 |        100094 | Product 94            | 100094 -Product 94  |            4400 | Subgroup 44            |          401 | Group 4             |             2 | Family 2             |
|        100074 |         200061 |               202108 |                  24260 |                 202202 |                   24266 |               615 |            627 | 154.0                  |              781 |                  645 |                        |            |              781 |        100074 | Product 74            | 100074 -Product 74  |            3700 | Subgroup 37            |          301 | Group 3             |             2 | Family 2             |
|        100087 |         200028 |               202108 |                  24260 |                 202206 |                   24270 |               453 |            462 |                        |              462 |                  476 |                        |            |              476 |        100087 | Product 87            | 100087 -Product 87  |            4200 | Subgroup 42            |          401 | Group 4             |             2 | Family 2             |
|        100095 |         200034 |               202108 |                  24260 |                 202208 |                   24272 |               587 |            599 |                        |              599 |                  616 |                        |            |              616 |        100095 | Product 95            | 100095 -Product 95  |            4500 | Subgroup 45            |          401 | Group 4             |             2 | Family 2             |
|        100068 |         200040 |               202108 |                  24260 |                 202210 |                   24274 |               549 |            560 |                        |              560 |                  577 |                        |            |              577 |        100068 | Product 68            | 100068 -Product 68  |            3500 | Subgroup 25            |          301 | Group 3             |             2 | Family 2             |
|        100018 |         200020 |               202108 |                  24260 |                 202203 |                   24267 |               420 |            428 | 105.0                  |              533 |                  441 |                        |            |              533 |        100018 | Product 18            | 100018 -Product 18  |            1600 | Subgroup 6             |          101 | Group 1             |             1 | Family 1             |
|        100018 |         200020 |               202108 |                  24260 |                 202204 |                   24268 |               400 |            408 |                        |              408 |                  420 |                        |            |              420 |        100018 | Product 18            | 100018 -Product 18  |            1600 | Subgroup 6             |          101 | Group 1             |             1 | Family 1             |
|        100074 |         200061 |               202108 |                  24260 |                 202210 |                   24274 |               635 |            648 |                        |              648 |                  667 |                        |            |              667 |        100074 | Product 74            | 100074 -Product 74  |            3700 | Subgroup 37            |          301 | Group 3             |             2 | Family 2             |
|        100094 |         200024 |               202108 |                  24260 |                 202205 |                   24269 |               800 |            816 |                        |              816 |                  840 |                        |            |              840 |        100094 | Product 94            | 100094 -Product 94  |            4400 | Subgroup 44            |          401 | Group 4             |             2 | Family 2             |
|        100075 |         200057 |               202108 |                  24260 |                 202111 |                   24263 |               693 |            707 | 173.0                  |              880 |                  728 |                        |            |              880 |        100075 | Product 75            | 100075 -Product 75  |            3700 | Subgroup 37            |          301 | Group 3             |             2 | Family 2             |
|        100094 |         200028 |               202108 |                  24260 |                 202202 |                   24266 |               430 |            439 | 108.0                  |              546 |                  452 |                        |            |              546 |        100094 | Product 94            | 100094 -Product 94  |            4400 | Subgroup 44            |          401 | Group 4             |             2 | Family 2             |
|        100034 |         200058 |               202108 |                  24260 |                 202110 |                   24262 |                90 |             92 | 22.0                   |              114 |                   94 |                        |            |              114 |        100034 | Product 34            | 100034 -Product 34  |            2200 | Subgroup 12            |          201 | Group 2             |             1 | Family 1             |
|        100094 |         200028 |               202108 |                  24260 |                 202108 |                   24260 |               100 |            102 | 25.0                   |              127 |                  105 |                        |            |              127 |        100094 | Product 94            | 100094 -Product 94  |            4400 | Subgroup 44            |          401 | Group 4             |             2 | Family 2             |
|        100055 |         200023 |               202108 |                  24260 |                 202111 |                   24263 |               200 |            204 | 50.0                   |              254 |                  210 |                        |            |              254 |        100055 | Product 55            | 100055 -Product 55  |            3000 | Subgroup 20            |          301 | Group 3             |             2 | Family 2             |
|        100031 |         200025 |               202108 |                  24260 |                 202207 |                   24271 |               150 |            153 |                        |              153 |                  158 |                        |            |              158 |        100031 | Product 31            | 100031 -Product 31  |            2100 | Subgroup 11            |          201 | Group 2             |             1 | Family 1             |
|        100075 |         200057 |               202108 |                  24260 |                 202206 |                   24270 |               711 |            725 |                        |              725 |                  746 |                        |            |              746 |        100075 | Product 75            | 100075 -Product 75  |            3700 | Subgroup 37            |          301 | Group 3             |             2 | Family 2             |
|        100068 |         200040 |               202108 |                  24260 |                 202205 |                   24269 |               536 |            547 |                        |              547 |                  563 |                        |            |              563 |        100068 | Product 68            | 100068 -Product 68  |            3500 | Subgroup 25            |          301 | Group 3             |             2 | Family 2             |
|        100018 |         200020 |               202108 |                  24260 |                 202210 |                   24274 |                90 |             92 |                        |               92 |                   94 |                        |            |               94 |        100018 | Product 18            | 100018 -Product 18  |            1600 | Subgroup 6             |          101 | Group 1             |             1 | Family 1             |
|        100084 |         200047 |               202108 |                  24260 |                 202210 |                   24274 |               335 |            341 |                        |              341 |                  351 |                        |            |              351 |        100084 | Product 84            | 100084 -Product 84  |            4100 | Subgroup 41            |          401 | Group 4             |             2 | Family 2             |
|        100047 |         200032 |               202108 |                  24260 |                 202208 |                   24272 |               140 |            143 |                        |              143 |                  147 |                        |            |              147 |        100047 | Product 47            | 100047 -Product 47  |            2700 | Subgroup 17            |          201 | Group 2             |             1 | Family 1             |
|        100001 |         200001 |               202108 |                  24260 |                 202204 |                   24268 |               400 |            408 |                        |              408 |                  420 |                        |            |              420 |        100001 | Product 1             | 100001 -Product 1   |            1100 | Subgroup 1             |          101 | Group 1             |             1 | Family 1             |
|        100059 |         200032 |               202108 |                  24260 |                 202211 |                   24275 |               294 |            300 |                        |              300 |                  309 |                        |            |              309 |        100059 | Product 59            | 100059 -Product 59  |            3100 | Subgroup 21            |          301 | Group 3             |             2 | Family 2             |
|        100093 |         200010 |               202108 |                  24260 |                 202201 |                   24265 |               150 |            153 | 38.0                   |              190 |                  158 |                        |            |              190 |        100093 | Product 93            | 100093 -Product 93  |            4400 | Subgroup 44            |          401 | Group 4             |             2 | Family 2             |
|        100094 |         200024 |               202108 |                  24260 |                 202109 |                   24261 |               110 |            112 | 28.0                   |              140 |                  116 |                        |            |              140 |        100094 | Product 94            | 100094 -Product 94  |            4400 | Subgroup 44            |          401 | Group 4             |             2 | Family 2             |
|        100094 |         200024 |               202108 |                  24260 |                 202206 |                   24270 |               410 |            418 |                        |              418 |                  430 |                        |            |              430 |        100094 | Product 94            | 100094 -Product 94  |            4400 | Subgroup 44            |          401 | Group 4             |             2 | Family 2             |
|        100066 |         200049 |               202108 |                  24260 |                 202110 |                   24262 |                90 |             92 | 22.0                   |              114 |                   94 |                        |            |              114 |        100066 | Product 66            | 100066 -Product 66  |            3400 | Subgroup 24            |          301 | Group 3             |             2 | Family 2             |
|        100031 |         200025 |               202108 |                  24260 |                 202205 |                   24269 |               800 |            816 |                        |              816 |                  840 |                        |            |              840 |        100031 | Product 31            | 100031 -Product 31  |            2100 | Subgroup 11            |          201 | Group 2             |             1 | Family 1             |
|        100059 |         200032 |               202108 |                  24260 |                 202202 |                   24266 |               271 |            277 | 68.0                   |              345 |                  285 |                        |            |              345 |        100059 | Product 59            | 100059 -Product 59  |            3100 | Subgroup 21            |          301 | Group 3             |             2 | Family 2             |
|        100047 |         200032 |               202108 |                  24260 |                 202111 |                   24263 |               200 |            204 | 50.0                   |              254 |                  210 |                        |            |              254 |        100047 | Product 47            | 100047 -Product 47  |            2700 | Subgroup 17            |          201 | Group 2             |             1 | Family 1             |
|        100095 |         200062 |               202108 |                  24260 |                 202201 |                   24265 |               483 |            493 | 121.0                  |              614 |                  508 |                        |            |              614 |        100095 | Product 95            | 100095 -Product 95  |            4500 | Subgroup 45            |          401 | Group 4             |             2 | Family 2             |
|        100095 |         200014 |               202108 |                  24260 |                 202209 |                   24273 |               375 |            382 |                        |              382 |                  394 |                        |            |              394 |        100095 | Product 95            | 100095 -Product 95  |            4500 | Subgroup 45            |          401 | Group 4             |             2 | Family 2             |
|        100066 |         200049 |               202108 |                  24260 |                 202210 |                   24274 |                90 |             92 |                        |               92 |                   94 |                        |            |               94 |        100066 | Product 66            | 100066 -Product 66  |            3400 | Subgroup 24            |          301 | Group 3             |             2 | Family 2             |
|        100055 |         200023 |               202108 |                  24260 |                 202206 |                   24270 |               410 |            418 |                        |              418 |                  430 |                        |            |              430 |        100055 | Product 55            | 100055 -Product 55  |            3000 | Subgroup 20            |          301 | Group 3             |             2 | Family 2             |
|        100055 |         200023 |               202108 |                  24260 |                 202203 |                   24267 |               420 |            428 | 105.0                  |              533 |                  441 |                        |            |              533 |        100055 | Product 55            | 100055 -Product 55  |            3000 | Subgroup 20            |          301 | Group 3             |             2 | Family 2             |
|        100034 |         200058 |               202108 |                  24260 |                 202211 |                   24275 |               210 |            214 |                        |              214 |                  220 |                        |            |              220 |        100034 | Product 34            | 100034 -Product 34  |            2200 | Subgroup 12            |          201 | Group 2             |             1 | Family 1             |
|        100068 |         200040 |               202108 |                  24260 |                 202110 |                   24262 |               519 |            529 | 130.0                  |              659 |                  545 |                        |            |              659 |        100068 | Product 68            | 100068 -Product 68  |            3500 | Subgroup 25            |          301 | Group 3             |             2 | Family 2             |
|        100068 |         200040 |               202108 |                  24260 |                 202206 |                   24270 |               539 |            550 |                        |              550 |                  566 |                        |            |              566 |        100068 | Product 68            | 100068 -Product 68  |            3500 | Subgroup 25            |          301 | Group 3             |             2 | Family 2             |
|        100084 |         200047 |               202108 |                  24260 |                 202204 |                   24268 |               319 |            326 |                        |              326 |                  335 |                        |            |              335 |        100084 | Product 84            | 100084 -Product 84  |            4100 | Subgroup 41            |          401 | Group 4             |             2 | Family 2             |



label: Productcode
ProductCode
Productcode
Product description
Productcode
Product code &
Productcode
Subgroup code
Productcode
Subgroup description
Productcode
Group code
Productcode
Group description
Productcode
Family code
Productcode
Family description
output: {"Functional-Dependency": [["Productcode", "ProductCode"], ["Productcode", "Product description"], ["Productcode", "Product code &"], ["Productcode", "Subgroup code"], ["Productcode", "Subgroup description"], ["Productcode", "Group code"], ["Productcode", "Group description"], ["Productcode", "Family code"], ["Productcode", "Family description"]]}
labeled_fds: Productcode
ProductCode
Productcode
Product description
Productcode
Product code &
Productcode
Subgroup code
Productcode
Subgroup description
Productcode
Group code
Productcode
Group description
Productcode
Family code
Productcode
Family description
Sales Last Year
Sales Actual
Sales Last Year
Foreacast proposal
Sales Actual
Foreacast proposal
Sales & Open_x
Sales Actual
Sales & Open_x
Foreacast proposal
Foreacast proposal
Sales Actual
Total Forecast
Sales Actual
Total Forecast
Sales & Open_x
source: $MMTU_HOME/resources/Relationship-finding/FD/330718118