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   |   Quantity | Date                    |   Year |   QuarterOfYear |   MonthOfYear |   DayOfMonth |   DateInt | MonthName   | MonthInCalendar   | QuarterInCalendar   |   DayInWeek | DayOfWeekName   | WeekEnding              |   Week Number |   MonthnYear |   QuarternYear |   ShortYear |   MonthOffset |
|:----------|-----------:|:------------------------|-------:|----------------:|--------------:|-------------:|----------:|:------------|:------------------|:--------------------|------------:|:----------------|:------------------------|--------------:|-------------:|---------------:|------------:|--------------:|
| B         |         12 | 2020-01-03 00:00:00.000 |   2020 |               1 |             1 |            3 |  20200103 | January     | Jan 2020          | Q1 2020             |           5 | Friday          | 2020-01-04 00:00:00.000 |             1 |     20200100 |       20200100 |          20 |            -3 |
| A         |         15 | 2020-03-03 00:00:00.000 |   2020 |               1 |             3 |            3 |  20200303 | March       | Mar 2020          | Q1 2020             |           2 | Tuesday         | 2020-03-07 00:00:00.000 |            10 |     20200300 |       20200100 |          20 |            -1 |
| B         |         16 | 2020-03-15 00:00:00.000 |   2020 |               1 |             3 |           15 |  20200315 | March       | Mar 2020          | Q1 2020             |           0 | Sunday          | 2020-03-21 00:00:00.000 |            12 |     20200300 |       20200100 |          20 |            -1 |
| A         |         15 | 2020-03-24 00:00:00.000 |   2020 |               1 |             3 |           24 |  20200324 | March       | Mar 2020          | Q1 2020             |           2 | Tuesday         | 2020-03-28 00:00:00.000 |            13 |     20200300 |       20200100 |          20 |            -1 |
| C         |         14 | 2020-03-03 00:00:00.000 |   2020 |               1 |             3 |            3 |  20200303 | March       | Mar 2020          | Q1 2020             |           2 | Tuesday         | 2020-03-07 00:00:00.000 |            10 |     20200300 |       20200100 |          20 |            -1 |
| C         |         15 | 2020-02-06 00:00:00.000 |   2020 |               1 |             2 |            6 |  20200206 | February    | Feb 2020          | Q1 2020             |           4 | Thursday        | 2020-02-08 00:00:00.000 |             6 |     20200200 |       20200100 |          20 |            -2 |
| A         |         13 | 2020-01-19 00:00:00.000 |   2020 |               1 |             1 |           19 |  20200119 | January     | Jan 2020          | Q1 2020             |           0 | Sunday          | 2020-01-25 00:00:00.000 |             4 |     20200100 |       20200100 |          20 |            -3 |
| B         |         15 | 2020-03-22 00:00:00.000 |   2020 |               1 |             3 |           22 |  20200322 | March       | Mar 2020          | Q1 2020             |           0 | Sunday          | 2020-03-28 00:00:00.000 |            13 |     20200300 |       20200100 |          20 |            -1 |
| C         |         13 | 2020-03-08 00:00:00.000 |   2020 |               1 |             3 |            8 |  20200308 | March       | Mar 2020          | Q1 2020             |           0 | Sunday          | 2020-03-14 00:00:00.000 |            11 |     20200300 |       20200100 |          20 |            -1 |
| A         |         10 | 2020-03-27 00:00:00.000 |   2020 |               1 |             3 |           27 |  20200327 | March       | Mar 2020          | Q1 2020             |           5 | Friday          | 2020-03-28 00:00:00.000 |            13 |     20200300 |       20200100 |          20 |            -1 |
| C         |         12 | 2020-03-06 00:00:00.000 |   2020 |               1 |             3 |            6 |  20200306 | March       | Mar 2020          | Q1 2020             |           5 | Friday          | 2020-03-07 00:00:00.000 |            10 |     20200300 |       20200100 |          20 |            -1 |
| B         |         10 | 2020-03-26 00:00:00.000 |   2020 |               1 |             3 |           26 |  20200326 | March       | Mar 2020          | Q1 2020             |           4 | Thursday        | 2020-03-28 00:00:00.000 |            13 |     20200300 |       20200100 |          20 |            -1 |
| C         |         16 | 2020-01-28 00:00:00.000 |   2020 |               1 |             1 |           28 |  20200128 | January     | Jan 2020          | Q1 2020             |           2 | Tuesday         | 2020-02-01 00:00:00.000 |             5 |     20200100 |       20200100 |          20 |            -3 |
| A         |         16 | 2020-01-25 00:00:00.000 |   2020 |               1 |             1 |           25 |  20200125 | January     | Jan 2020          | Q1 2020             |           6 | Saturday        | 2020-01-25 00:00:00.000 |             4 |     20200100 |       20200100 |          20 |            -3 |
| B         |         16 | 2020-03-09 00:00:00.000 |   2020 |               1 |             3 |            9 |  20200309 | March       | Mar 2020          | Q1 2020             |           1 | Monday          | 2020-03-14 00:00:00.000 |            11 |     20200300 |       20200100 |          20 |            -1 |
| A         |         15 | 2020-02-14 00:00:00.000 |   2020 |               1 |             2 |           14 |  20200214 | February    | Feb 2020          | Q1 2020             |           5 | Friday          | 2020-02-15 00:00:00.000 |             7 |     20200200 |       20200100 |          20 |            -2 |
| B         |         15 | 2020-03-08 00:00:00.000 |   2020 |               1 |             3 |            8 |  20200308 | March       | Mar 2020          | Q1 2020             |           0 | Sunday          | 2020-03-14 00:00:00.000 |            11 |     20200300 |       20200100 |          20 |            -1 |
| C         |         12 | 2020-01-10 00:00:00.000 |   2020 |               1 |             1 |           10 |  20200110 | January     | Jan 2020          | Q1 2020             |           5 | Friday          | 2020-01-11 00:00:00.000 |             2 |     20200100 |       20200100 |          20 |            -3 |
| B         |         15 | 2020-03-19 00:00:00.000 |   2020 |               1 |             3 |           19 |  20200319 | March       | Mar 2020          | Q1 2020             |           4 | Thursday        | 2020-03-21 00:00:00.000 |            12 |     20200300 |       20200100 |          20 |            -1 |
| C         |         16 | 2020-02-14 00:00:00.000 |   2020 |               1 |             2 |           14 |  20200214 | February    | Feb 2020          | Q1 2020             |           5 | Friday          | 2020-02-15 00:00:00.000 |             7 |     20200200 |       20200100 |          20 |            -2 |
| B         |         12 | 2020-02-18 00:00:00.000 |   2020 |               1 |             2 |           18 |  20200218 | February    | Feb 2020          | Q1 2020             |           2 | Tuesday         | 2020-02-22 00:00:00.000 |             8 |     20200200 |       20200100 |          20 |            -2 |
| C         |         12 | 2020-02-15 00:00:00.000 |   2020 |               1 |             2 |           15 |  20200215 | February    | Feb 2020          | Q1 2020             |           6 | Saturday        | 2020-02-15 00:00:00.000 |             7 |     20200200 |       20200100 |          20 |            -2 |
| B         |         13 | 2020-02-20 00:00:00.000 |   2020 |               1 |             2 |           20 |  20200220 | February    | Feb 2020          | Q1 2020             |           4 | Thursday        | 2020-02-22 00:00:00.000 |             8 |     20200200 |       20200100 |          20 |            -2 |
| C         |         14 | 2020-03-09 00:00:00.000 |   2020 |               1 |             3 |            9 |  20200309 | March       | Mar 2020          | Q1 2020             |           1 | Monday          | 2020-03-14 00:00:00.000 |            11 |     20200300 |       20200100 |          20 |            -1 |
| C         |         13 | 2020-03-30 00:00:00.000 |   2020 |               1 |             3 |           30 |  20200330 | March       | Mar 2020          | Q1 2020             |           1 | Monday          | 2020-04-04 00:00:00.000 |            14 |     20200300 |       20200100 |          20 |            -1 |
| B         |         10 | 2020-04-01 00:00:00.000 |   2020 |               2 |             4 |            1 |  20200401 | April       | Apr 2020          | Q2 2020             |           3 | Wednesday       | 2020-04-04 00:00:00.000 |            14 |     20200400 |       20200200 |          20 |             0 |
| C         |         12 | 2020-03-27 00:00:00.000 |   2020 |               1 |             3 |           27 |  20200327 | March       | Mar 2020          | Q1 2020             |           5 | Friday          | 2020-03-28 00:00:00.000 |            13 |     20200300 |       20200100 |          20 |            -1 |
| B         |         12 | 2020-02-10 00:00:00.000 |   2020 |               1 |             2 |           10 |  20200210 | February    | Feb 2020          | Q1 2020             |           1 | Monday          | 2020-02-15 00:00:00.000 |             7 |     20200200 |       20200100 |          20 |            -2 |
| A         |         12 | 2020-01-30 00:00:00.000 |   2020 |               1 |             1 |           30 |  20200130 | January     | Jan 2020          | Q1 2020             |           4 | Thursday        | 2020-02-01 00:00:00.000 |             5 |     20200100 |       20200100 |          20 |            -3 |
| A         |         15 | 2020-02-20 00:00:00.000 |   2020 |               1 |             2 |           20 |  20200220 | February    | Feb 2020          | Q1 2020             |           4 | Thursday        | 2020-02-22 00:00:00.000 |             8 |     20200200 |       20200100 |          20 |            -2 |
| A         |         12 | 2020-03-06 00:00:00.000 |   2020 |               1 |             3 |            6 |  20200306 | March       | Mar 2020          | Q1 2020             |           5 | Friday          | 2020-03-07 00:00:00.000 |            10 |     20200300 |       20200100 |          20 |            -1 |
| B         |         10 | 2020-01-10 00:00:00.000 |   2020 |               1 |             1 |           10 |  20200110 | January     | Jan 2020          | Q1 2020             |           5 | Friday          | 2020-01-11 00:00:00.000 |             2 |     20200100 |       20200100 |          20 |            -3 |
| A         |         12 | 2020-03-14 00:00:00.000 |   2020 |               1 |             3 |           14 |  20200314 | March       | Mar 2020          | Q1 2020             |           6 | Saturday        | 2020-03-14 00:00:00.000 |            11 |     20200300 |       20200100 |          20 |            -1 |
| B         |         15 | 2020-01-29 00:00:00.000 |   2020 |               1 |             1 |           29 |  20200129 | January     | Jan 2020          | Q1 2020             |           3 | Wednesday       | 2020-02-01 00:00:00.000 |             5 |     20200100 |       20200100 |          20 |            -3 |
| C         |         15 | 2020-01-20 00:00:00.000 |   2020 |               1 |             1 |           20 |  20200120 | January     | Jan 2020          | Q1 2020             |           1 | Monday          | 2020-01-25 00:00:00.000 |             4 |     20200100 |       20200100 |          20 |            -3 |
| C         |         12 | 2020-02-21 00:00:00.000 |   2020 |               1 |             2 |           21 |  20200221 | February    | Feb 2020          | Q1 2020             |           5 | Friday          | 2020-02-22 00:00:00.000 |             8 |     20200200 |       20200100 |          20 |            -2 |
| C         |         13 | 2020-02-02 00:00:00.000 |   2020 |               1 |             2 |            2 |  20200202 | February    | Feb 2020          | Q1 2020             |           0 | Sunday          | 2020-02-08 00:00:00.000 |             6 |     20200200 |       20200100 |          20 |            -2 |
| C         |         10 | 2020-02-05 00:00:00.000 |   2020 |               1 |             2 |            5 |  20200205 | February    | Feb 2020          | Q1 2020             |           3 | Wednesday       | 2020-02-08 00:00:00.000 |             6 |     20200200 |       20200100 |          20 |            -2 |
| A         |         12 | 2020-01-20 00:00:00.000 |   2020 |               1 |             1 |           20 |  20200120 | January     | Jan 2020          | Q1 2020             |           1 | Monday          | 2020-01-25 00:00:00.000 |             4 |     20200100 |       20200100 |          20 |            -3 |
| C         |         12 | 2020-02-01 00:00:00.000 |   2020 |               1 |             2 |            1 |  20200201 | February    | Feb 2020          | Q1 2020             |           6 | Saturday        | 2020-02-01 00:00:00.000 |             5 |     20200200 |       20200100 |          20 |            -2 |
| B         |         12 | 2020-02-22 00:00:00.000 |   2020 |               1 |             2 |           22 |  20200222 | February    | Feb 2020          | Q1 2020             |           6 | Saturday        | 2020-02-22 00:00:00.000 |             8 |     20200200 |       20200100 |          20 |            -2 |
| B         |         14 | 2020-02-13 00:00:00.000 |   2020 |               1 |             2 |           13 |  20200213 | February    | Feb 2020          | Q1 2020             |           4 | Thursday        | 2020-02-15 00:00:00.000 |             7 |     20200200 |       20200100 |          20 |            -2 |
| C         |         12 | 2020-01-27 00:00:00.000 |   2020 |               1 |             1 |           27 |  20200127 | January     | Jan 2020          | Q1 2020             |           1 | Monday          | 2020-02-01 00:00:00.000 |             5 |     20200100 |       20200100 |          20 |            -3 |
| A         |         12 | 2020-03-16 00:00:00.000 |   2020 |               1 |             3 |           16 |  20200316 | March       | Mar 2020          | Q1 2020             |           1 | Monday          | 2020-03-21 00:00:00.000 |            12 |     20200300 |       20200100 |          20 |            -1 |
| A         |         10 | 2020-03-02 00:00:00.000 |   2020 |               1 |             3 |            2 |  20200302 | March       | Mar 2020          | Q1 2020             |           1 | Monday          | 2020-03-07 00:00:00.000 |            10 |     20200300 |       20200100 |          20 |            -1 |
| B         |         13 | 2020-01-23 00:00:00.000 |   2020 |               1 |             1 |           23 |  20200123 | January     | Jan 2020          | Q1 2020             |           4 | Thursday        | 2020-01-25 00:00:00.000 |             4 |     20200100 |       20200100 |          20 |            -3 |
| A         |         12 | 2020-02-27 00:00:00.000 |   2020 |               1 |             2 |           27 |  20200227 | February    | Feb 2020          | Q1 2020             |           4 | Thursday        | 2020-02-29 00:00:00.000 |             9 |     20200200 |       20200100 |          20 |            -2 |
| C         |         12 | 2020-03-18 00:00:00.000 |   2020 |               1 |             3 |           18 |  20200318 | March       | Mar 2020          | Q1 2020             |           3 | Wednesday       | 2020-03-21 00:00:00.000 |            12 |     20200300 |       20200100 |          20 |            -1 |
| B         |         14 | 2020-02-04 00:00:00.000 |   2020 |               1 |             2 |            4 |  20200204 | February    | Feb 2020          | Q1 2020             |           2 | Tuesday         | 2020-02-08 00:00:00.000 |             6 |     20200200 |       20200100 |          20 |            -2 |
| C         |         14 | 2020-03-24 00:00:00.000 |   2020 |               1 |             3 |           24 |  20200324 | March       | Mar 2020          | Q1 2020             |           2 | Tuesday         | 2020-03-28 00:00:00.000 |            13 |     20200300 |       20200100 |          20 |            -1 |



label: Date
Year
Date
QuarterOfYear
Date
MonthOfYear
Date
DayOfMonth
Date
DateInt
Date
MonthName
Date
MonthInCalendar
Date
QuarterInCalendar
Date
DayInWeek
Date
DayOfWeekName
Date
WeekEnding
Date
Week Number
Date
MonthnYear
Date
QuarternYear
Date
ShortYear
Date
MonthOffset
output: {"Functional-Dependency": [["Date", "Year"], ["Date", "QuarterOfYear"], ["Date", "MonthOfYear"], ["Date", "DayOfMonth"], ["Date", "DateInt"], ["Date", "MonthName"], ["Date", "MonthInCalendar"], ["Date", "QuarterInCalendar"], ["Date", "DayInWeek"], ["Date", "DayOfWeekName"], ["Date", "WeekEnding"], ["Date", "Week Number"], ["Date", "MonthnYear"], ["Date", "QuarternYear"], ["Date", "ShortYear"], ["Date", "MonthOffset"]]}
labeled_fds: Date
Year
Date
QuarterOfYear
Date
MonthOfYear
Date
DayOfMonth
Date
DateInt
Date
MonthName
Date
MonthInCalendar
Date
QuarterInCalendar
Date
DayInWeek
Date
DayOfWeekName
Date
WeekEnding
Date
Week Number
Date
MonthnYear
Date
QuarternYear
Date
ShortYear
Date
MonthOffset
DayOfMonth
QuarterInCalendar
DayOfMonth
QuarternYear
DayOfWeekName
QuarterOfYear
WeekEnding
MonthInCalendar
WeekEnding
QuarterInCalendar
WeekEnding
QuarternYear
source: $MMTU_HOME/resources/Relationship-finding/FD/195293277