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:
| Date                    |   Year |   Month |   WeekNum |   Day |   WeekDay | Quarter   | ShortMonth   | ShortMonth Day   |   month | shortMonth   | longMonth   |   quarter |
|:------------------------|-------:|--------:|----------:|------:|----------:|:----------|:-------------|:-----------------|--------:|:-------------|:------------|----------:|
| 2021-12-04 00:00:00.000 |   2021 |      12 |        49 |     4 |         7 | 2021 Q4   | 2021 Dec     | Dec 4            |      12 | Dec          | December    |         4 |
| 2020-02-03 00:00:00.000 |   2020 |       2 |         6 |     3 |         2 | 2020 Q1   | 2020 Feb     | Feb 3            |       2 | Feb          | February    |         1 |
| 2020-10-27 00:00:00.000 |   2020 |      10 |        44 |    27 |         3 | 2020 Q4   | 2020 Oct     | Oct 27           |      10 | Oct          | October     |         4 |
| 2021-04-01 00:00:00.000 |   2021 |       4 |        14 |     1 |         5 | 2021 Q2   | 2021 Apr     | Apr 1            |       4 | Apr          | April       |         2 |
| 2021-09-25 00:00:00.000 |   2021 |       9 |        39 |    25 |         7 | 2021 Q3   | 2021 Sep     | Sep 25           |       9 | Sep          | September   |         3 |
| 2021-07-11 00:00:00.000 |   2021 |       7 |        29 |    11 |         1 | 2021 Q3   | 2021 Jul     | Jul 11           |       7 | Jul          | July        |         3 |
| 2020-02-09 00:00:00.000 |   2020 |       2 |         7 |     9 |         1 | 2020 Q1   | 2020 Feb     | Feb 9            |       2 | Feb          | February    |         1 |
| 2020-12-22 00:00:00.000 |   2020 |      12 |        52 |    22 |         3 | 2020 Q4   | 2020 Dec     | Dec 22           |      12 | Dec          | December    |         4 |
| 2021-07-13 00:00:00.000 |   2021 |       7 |        29 |    13 |         3 | 2021 Q3   | 2021 Jul     | Jul 13           |       7 | Jul          | July        |         3 |
| 2021-05-29 00:00:00.000 |   2021 |       5 |        22 |    29 |         7 | 2021 Q2   | 2021 May     | May 29           |       5 | May          | May         |         2 |
| 2021-12-30 00:00:00.000 |   2021 |      12 |        53 |    30 |         5 | 2021 Q4   | 2021 Dec     | Dec 30           |      12 | Dec          | December    |         4 |
| 2020-12-21 00:00:00.000 |   2020 |      12 |        52 |    21 |         2 | 2020 Q4   | 2020 Dec     | Dec 21           |      12 | Dec          | December    |         4 |
| 2020-06-13 00:00:00.000 |   2020 |       6 |        24 |    13 |         7 | 2020 Q2   | 2020 Jun     | Jun 13           |       6 | Jun          | June        |         2 |
| 2021-11-28 00:00:00.000 |   2021 |      11 |        49 |    28 |         1 | 2021 Q4   | 2021 Nov     | Nov 28           |      11 | Nov          | November    |         4 |
| 2020-03-07 00:00:00.000 |   2020 |       3 |        10 |     7 |         7 | 2020 Q1   | 2020 Mar     | Mar 7            |       3 | Mar          | March       |         1 |
| 2020-03-19 00:00:00.000 |   2020 |       3 |        12 |    19 |         5 | 2020 Q1   | 2020 Mar     | Mar 19           |       3 | Mar          | March       |         1 |
| 2020-03-13 00:00:00.000 |   2020 |       3 |        11 |    13 |         6 | 2020 Q1   | 2020 Mar     | Mar 13           |       3 | Mar          | March       |         1 |
| 2021-10-05 00:00:00.000 |   2021 |      10 |        41 |     5 |         3 | 2021 Q4   | 2021 Oct     | Oct 5            |      10 | Oct          | October     |         4 |
| 2020-06-30 00:00:00.000 |   2020 |       6 |        27 |    30 |         3 | 2020 Q2   | 2020 Jun     | Jun 30           |       6 | Jun          | June        |         2 |
| 2021-01-15 00:00:00.000 |   2021 |       1 |         3 |    15 |         6 | 2021 Q1   | 2021 Jan     | Jan 15           |       1 | Jan          | January     |         1 |
| 2021-08-29 00:00:00.000 |   2021 |       8 |        36 |    29 |         1 | 2021 Q3   | 2021 Aug     | Aug 29           |       8 | Aug          | August      |         3 |
| 2021-06-29 00:00:00.000 |   2021 |       6 |        27 |    29 |         3 | 2021 Q2   | 2021 Jun     | Jun 29           |       6 | Jun          | June        |         2 |
| 2021-04-12 00:00:00.000 |   2021 |       4 |        16 |    12 |         2 | 2021 Q2   | 2021 Apr     | Apr 12           |       4 | Apr          | April       |         2 |
| 2020-03-06 00:00:00.000 |   2020 |       3 |        10 |     6 |         6 | 2020 Q1   | 2020 Mar     | Mar 6            |       3 | Mar          | March       |         1 |
| 2020-02-24 00:00:00.000 |   2020 |       2 |         9 |    24 |         2 | 2020 Q1   | 2020 Feb     | Feb 24           |       2 | Feb          | February    |         1 |
| 2020-08-23 00:00:00.000 |   2020 |       8 |        35 |    23 |         1 | 2020 Q3   | 2020 Aug     | Aug 23           |       8 | Aug          | August      |         3 |
| 2020-03-22 00:00:00.000 |   2020 |       3 |        13 |    22 |         1 | 2020 Q1   | 2020 Mar     | Mar 22           |       3 | Mar          | March       |         1 |
| 2021-09-24 00:00:00.000 |   2021 |       9 |        39 |    24 |         6 | 2021 Q3   | 2021 Sep     | Sep 24           |       9 | Sep          | September   |         3 |
| 2021-02-08 00:00:00.000 |   2021 |       2 |         7 |     8 |         2 | 2021 Q1   | 2021 Feb     | Feb 8            |       2 | Feb          | February    |         1 |
| 2021-12-18 00:00:00.000 |   2021 |      12 |        51 |    18 |         7 | 2021 Q4   | 2021 Dec     | Dec 18           |      12 | Dec          | December    |         4 |
| 2020-12-10 00:00:00.000 |   2020 |      12 |        50 |    10 |         5 | 2020 Q4   | 2020 Dec     | Dec 10           |      12 | Dec          | December    |         4 |
| 2020-10-13 00:00:00.000 |   2020 |      10 |        42 |    13 |         3 | 2020 Q4   | 2020 Oct     | Oct 13           |      10 | Oct          | October     |         4 |
| 2021-04-25 00:00:00.000 |   2021 |       4 |        18 |    25 |         1 | 2021 Q2   | 2021 Apr     | Apr 25           |       4 | Apr          | April       |         2 |
| 2021-06-07 00:00:00.000 |   2021 |       6 |        24 |     7 |         2 | 2021 Q2   | 2021 Jun     | Jun 7            |       6 | Jun          | June        |         2 |
| 2021-04-10 00:00:00.000 |   2021 |       4 |        15 |    10 |         7 | 2021 Q2   | 2021 Apr     | Apr 10           |       4 | Apr          | April       |         2 |
| 2021-03-24 00:00:00.000 |   2021 |       3 |        13 |    24 |         4 | 2021 Q1   | 2021 Mar     | Mar 24           |       3 | Mar          | March       |         1 |
| 2021-08-24 00:00:00.000 |   2021 |       8 |        35 |    24 |         3 | 2021 Q3   | 2021 Aug     | Aug 24           |       8 | Aug          | August      |         3 |
| 2021-08-25 00:00:00.000 |   2021 |       8 |        35 |    25 |         4 | 2021 Q3   | 2021 Aug     | Aug 25           |       8 | Aug          | August      |         3 |
| 2020-11-22 00:00:00.000 |   2020 |      11 |        48 |    22 |         1 | 2020 Q4   | 2020 Nov     | Nov 22           |      11 | Nov          | November    |         4 |
| 2020-01-11 00:00:00.000 |   2020 |       1 |         2 |    11 |         7 | 2020 Q1   | 2020 Jan     | Jan 11           |       1 | Jan          | January     |         1 |
| 2020-04-19 00:00:00.000 |   2020 |       4 |        17 |    19 |         1 | 2020 Q2   | 2020 Apr     | Apr 19           |       4 | Apr          | April       |         2 |
| 2021-03-06 00:00:00.000 |   2021 |       3 |        10 |     6 |         7 | 2021 Q1   | 2021 Mar     | Mar 6            |       3 | Mar          | March       |         1 |
| 2021-08-01 00:00:00.000 |   2021 |       8 |        32 |     1 |         1 | 2021 Q3   | 2021 Aug     | Aug 1            |       8 | Aug          | August      |         3 |
| 2020-06-04 00:00:00.000 |   2020 |       6 |        23 |     4 |         5 | 2020 Q2   | 2020 Jun     | Jun 4            |       6 | Jun          | June        |         2 |
| 2021-07-23 00:00:00.000 |   2021 |       7 |        30 |    23 |         6 | 2021 Q3   | 2021 Jul     | Jul 23           |       7 | Jul          | July        |         3 |
| 2020-12-06 00:00:00.000 |   2020 |      12 |        50 |     6 |         1 | 2020 Q4   | 2020 Dec     | Dec 6            |      12 | Dec          | December    |         4 |
| 2020-07-17 00:00:00.000 |   2020 |       7 |        29 |    17 |         6 | 2020 Q3   | 2020 Jul     | Jul 17           |       7 | Jul          | July        |         3 |
| 2021-03-12 00:00:00.000 |   2021 |       3 |        11 |    12 |         6 | 2021 Q1   | 2021 Mar     | Mar 12           |       3 | Mar          | March       |         1 |
| 2021-05-28 00:00:00.000 |   2021 |       5 |        22 |    28 |         6 | 2021 Q2   | 2021 May     | May 28           |       5 | May          | May         |         2 |
| 2021-03-25 00:00:00.000 |   2021 |       3 |        13 |    25 |         5 | 2021 Q1   | 2021 Mar     | Mar 25           |       3 | Mar          | March       |         1 |



label: Month
month
Month
shortMonth
Month
longMonth
Month
quarter
output: {"Functional-Dependency": [["Month", "month"], ["Month", "shortMonth"], ["Month", "longMonth"], ["Month", "quarter"]]}
labeled_fds: Month
month
Month
shortMonth
Month
longMonth
Month
quarter
ShortMonth Day
WeekNum
source: $MMTU_HOME/resources/Relationship-finding/FD/173883755