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:
|   product_id | month   | sales_no   |   return | Province         | Month   |   Month_Index |
|-------------:|:--------|:-----------|---------:|:-----------------|:--------|--------------:|
|       352846 | Mar     | CA010      |        0 | Alberta          | Mar     |             3 |
|       292158 | Apr     | CA014      |        1 | Manitoba         | Apr     |             4 |
|       462356 | June    | CA010      |        0 | Alberta          | June    |             6 |
|       146487 | Mar     | CA008      |        0 | Ontario          | Mar     |             3 |
|       102974 | July    | CA003      |        0 | Nova Scotia      | July    |             7 |
|       890038 | Oct     | CA014      |        1 | Manitoba         | Oct     |            10 |
|       705118 | Oct     | CA010      |        1 | Alberta          | Oct     |            10 |
|       106548 | Nov     | CA005      |        0 | British Columbia | Nov     |            11 |
|       908629 | July    | CA004      |        1 | Ontario          | July    |             7 |
|       478171 | Nov     | CA003      |        0 | Nova Scotia      | Nov     |            11 |
|       467934 | Jan     | CA011      |        0 | Nova Scotia      | Jan     |             1 |
|       124988 | Mar     | CA001      |        0 | Ontario          | Mar     |             3 |
|       729311 | July    | CA012      |        0 | Ontario          | July    |             7 |
|       422278 | Nov     | CA010      |        0 | Alberta          | Nov     |            11 |
|       806750 | Nov     | CA007      |        0 | New Brunswick    | Nov     |            11 |
|       264121 | Oct     | CA009      |        0 | Ontario          | Oct     |            10 |
|       459741 | Jan     | CA016      |        1 | Ontario          | Jan     |             1 |
|       867053 | Mar     | CA004      |        1 | Ontario          | Mar     |             3 |
|       126725 | Aug     | CA007      |        0 | New Brunswick    | Aug     |             8 |
|       920276 | July    | CA003      |        0 | Nova Scotia      | July    |             7 |
|       248942 | Mar     | CA001      |        0 | Ontario          | Mar     |             3 |
|       510009 | Nov     | CA008      |        0 | Ontario          | Nov     |            11 |
|       314808 | Oct     | CA009      |        0 | Ontario          | Oct     |            10 |
|       747647 | Oct     | CA005      |        0 | British Columbia | Oct     |            10 |
|       396022 | Jan     | CA010      |        1 | Alberta          | Jan     |             1 |
|       524000 | Feb     | CA015      |        0 | New Brunswick    | Feb     |             2 |
|       275316 | June    | CA007      |        0 | New Brunswick    | June    |             6 |
|       321517 | Dec     | CA006      |        1 | Manitoba         | Dec     |            12 |
|       698530 | Dec     | CA008      |        0 | Ontario          | Dec     |            12 |
|       975358 | Sept    | CA006      |        1 | Manitoba         | Sept    |             9 |
|       929001 | May     | CA016      |        0 | Ontario          | May     |             5 |
|       351261 | Apr     | CA002      |        0 | Alberta          | Apr     |             4 |
|       732300 | June    | CA012      |        1 | Ontario          | June    |             6 |
|       620945 | Nov     | CA015      |        0 | New Brunswick    | Nov     |            11 |
|       698390 | Jan     | CA008      |        0 | Ontario          | Jan     |             1 |
|       490710 | Sept    | CA009      |        0 | Ontario          | Sept    |             9 |
|       294798 | July    | CA005      |        0 | British Columbia | July    |             7 |
|       738968 | Dec     | CA008      |        1 | Ontario          | Dec     |            12 |
|       631909 | Aug     | CA008      |        0 | Ontario          | Aug     |             8 |
|       996724 | Aug     | CA002      |        1 | Alberta          | Aug     |             8 |
|       551538 | Apr     | CA001      |        0 | Ontario          | Apr     |             4 |
|       963306 | July    | CA001      |        0 | Ontario          | July    |             7 |
|       437672 | Sept    | CA008      |        1 | Ontario          | Sept    |             9 |
|       840502 | July    | CA012      |        1 | Ontario          | July    |             7 |
|       950187 | June    | CA014      |        0 | Manitoba         | June    |             6 |
|       166010 | Jan     | CA014      |        0 | Manitoba         | Jan     |             1 |
|       569776 | Apr     | CA003      |        0 | Nova Scotia      | Apr     |             4 |
|       549861 | Jan     | CA001      |        0 | Ontario          | Jan     |             1 |
|       190724 | May     | CA003      |        0 | Nova Scotia      | May     |             5 |
|       935553 | Oct     | CA014      |        0 | Manitoba         | Oct     |            10 |



label: month
Month
month
Month_Index
output: {"Functional-Dependency": [["month", "Month"], ["month", "Month_Index"]]}
labeled_fds: month
Month
month
Month_Index
product_id
month
product_id
sales_no
product_id
return
product_id
Province
product_id
Month
product_id
Month_Index
source: $MMTU_HOME/resources/Relationship-finding/FD/313817044