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:
|   EmployeeKey |   PayrollDateKey |   TimesheetID |   TimesheetHours |   TimesheetTotalPay |   DateKey | Date                    | FullDateUSA   |   DayOfWeek | DayName   |   DayOfMonth |   DayOfYear |   WeekOfYear | MonthName   |   MonthOfYear |   Quarter | QuarterName   |   Year | IsWeekday   |
|--------------:|-----------------:|--------------:|-----------------:|--------------------:|----------:|:------------------------|:--------------|------------:|:----------|-------------:|------------:|-------------:|:------------|--------------:|----------:|:--------------|-------:|:------------|
|            25 |         20110912 |          2578 |               40 |              440.55 |  20110912 | 2011-09-12 00:00:00.000 | 09/12/2011    |           2 | Monday    |           12 |         255 |           38 | September   |             9 |         3 | Third         |   2011 | True        |
|            27 |         20111024 |          2766 |               40 |              776.02 |  20111024 | 2011-10-24 00:00:00.000 | 10/24/2011    |           2 | Monday    |           24 |         297 |           44 | October     |            10 |         4 | Fourth        |   2011 | True        |
|            14 |         20110718 |          2325 |               40 |              596.16 |  20110718 | 2011-07-18 00:00:00.000 | 07/18/2011    |           2 | Monday    |           18 |         199 |           30 | July        |             7 |         3 | Third         |   2011 | True        |
|            25 |         20120130 |          3198 |               40 |              453.78 |  20120130 | 2012-01-30 00:00:00.000 | 01/30/2012    |           2 | Monday    |           30 |          30 |            5 | January     |             1 |         1 | First         |   2012 | True        |
|            25 |         20131118 |          6112 |               40 |              464.34 |  20131118 | 2013-11-18 00:00:00.000 | 11/18/2013    |           2 | Monday    |           18 |         322 |           47 | November    |            11 |         4 | Fourth        |   2013 | True        |
|            20 |         20120319 |          3410 |               40 |              813.88 |  20120319 | 2012-03-19 00:00:00.000 | 03/19/2012    |           2 | Monday    |           19 |          79 |           12 | March       |             3 |         1 | First         |   2012 | True        |
|            20 |         20100906 |          1016 |               40 |              782    |  20100906 | 2010-09-06 00:00:00.000 | 09/06/2010    |           2 | Monday    |            6 |         249 |           37 | September   |             9 |         3 | Third         |   2010 | True        |
|            12 |         20100405 |           374 |               40 |              410    |  20100405 | 2010-04-05 00:00:00.000 | 04/05/2010    |           2 | Monday    |            5 |          95 |           15 | April       |             4 |         2 | Second        |   2010 | True        |
|             1 |         20130211 |          4850 |               20 |              305.66 |  20130211 | 2013-02-11 00:00:00.000 | 02/11/2013    |           2 | Monday    |           11 |          42 |            7 | February    |             2 |         1 | First         |   2013 | True        |
|             6 |         20121015 |          4327 |               40 |              726.46 |  20121015 | 2012-10-15 00:00:00.000 | 10/15/2012    |           2 | Monday    |           15 |         289 |           42 | October     |            10 |         4 | Fourth        |   2012 | True        |
|             6 |         20130708 |          5505 |               40 |              743.38 |  20130708 | 2013-07-08 00:00:00.000 | 07/08/2013    |           2 | Monday    |            8 |         189 |           28 | July        |             7 |         3 | Third         |   2013 | True        |
|            27 |         20120716 |          3944 |               40 |              799.32 |  20120716 | 2012-07-16 00:00:00.000 | 07/16/2012    |           2 | Monday    |           16 |         198 |           29 | July        |             7 |         3 | Third         |   2012 | True        |
|            26 |         20100524 |           586 |               19 |              190    |  20100524 | 2010-05-24 00:00:00.000 | 05/24/2010    |           2 | Monday    |           24 |         144 |           22 | May         |             5 |         2 | Second        |   2010 | True        |
|            23 |         20130422 |          5180 |               13 |              156.44 |  20130422 | 2013-04-22 00:00:00.000 | 04/22/2013    |           2 | Monday    |           22 |         112 |           17 | April       |             4 |         2 | Second        |   2013 | True        |
|             4 |         20120820 |          4077 |               40 |              512.06 |  20120820 | 2012-08-20 00:00:00.000 | 08/20/2012    |           2 | Monday    |           20 |         233 |           34 | August      |             8 |         3 | Third         |   2012 | True        |
|             6 |         20110613 |          2172 |               40 |              705.29 |  20110613 | 2011-06-13 00:00:00.000 | 06/13/2011    |           2 | Monday    |           13 |         164 |           25 | June        |             6 |         2 | Second        |   2011 | True        |
|             1 |         20130909 |          5780 |               20 |              305.66 |  20130909 | 2013-09-09 00:00:00.000 | 09/09/2013    |           2 | Monday    |            9 |         252 |           37 | September   |             9 |         3 | Third         |   2013 | True        |
|             8 |         20130729 |          5600 |               40 |              494.16 |  20130729 | 2013-07-29 00:00:00.000 | 07/29/2013    |           2 | Monday    |           29 |         210 |           31 | July        |             7 |         3 | Third         |   2013 | True        |
|             9 |         20131202 |          6159 |               40 |              468.6  |  20131202 | 2013-12-02 00:00:00.000 | 12/02/2013    |           2 | Monday    |            2 |         336 |           49 | December    |            12 |         4 | Fourth        |   2013 | True        |
|            15 |         20131209 |          6195 |               21 |              235.95 |  20131209 | 2013-12-09 00:00:00.000 | 12/09/2013    |           2 | Monday    |            9 |         343 |           50 | December    |            12 |         4 | Fourth        |   2013 | True        |
|            14 |         20120213 |          3249 |               40 |              614.06 |  20120213 | 2012-02-13 00:00:00.000 | 02/13/2012    |           2 | Monday    |           13 |          44 |            7 | February    |             2 |         1 | First         |   2012 | True        |
|             5 |         20120213 |          3241 |               40 |              786.82 |  20120213 | 2012-02-13 00:00:00.000 | 02/13/2012    |           2 | Monday    |           13 |          44 |            7 | February    |             2 |         1 | First         |   2012 | True        |
|             1 |         20130225 |          4912 |               14 |              213.96 |  20130225 | 2013-02-25 00:00:00.000 | 02/25/2013    |           2 | Monday    |           25 |          56 |            9 | February    |             2 |         1 | First         |   2013 | True        |
|            33 |         20100816 |           941 |               40 |             2754    |  20100816 | 2010-08-16 00:00:00.000 | 08/16/2010    |           2 | Monday    |           16 |         228 |           34 | August      |             8 |         3 | Third         |   2010 | True        |
|            32 |         20130916 |          5840 |               40 |             1214.11 |  20130916 | 2013-09-16 00:00:00.000 | 09/16/2013    |           2 | Monday    |           16 |         259 |           38 | September   |             9 |         3 | Third         |   2013 | True        |
|            31 |         20110822 |          2492 |               40 |              868.98 |  20110822 | 2011-08-22 00:00:00.000 | 08/22/2011    |           2 | Monday    |           22 |         234 |           35 | August      |             8 |         3 | Third         |   2011 | True        |
|             2 |         20100614 |           652 |               40 |              566    |  20100614 | 2010-06-14 00:00:00.000 | 06/14/2010    |           2 | Monday    |           14 |         165 |           25 | June        |             6 |         2 | Second        |   2010 | True        |
|            31 |         20131007 |          5932 |               40 |              915.9  |  20131007 | 2013-10-07 00:00:00.000 | 10/07/2013    |           2 | Monday    |            7 |         280 |           41 | October     |            10 |         4 | Fourth        |   2013 | True        |
|            14 |         20130318 |          5016 |               40 |              628.35 |  20130318 | 2013-03-18 00:00:00.000 | 03/18/2013    |           2 | Monday    |           18 |          77 |           12 | March       |             3 |         1 | First         |   2013 | True        |
|             4 |         20110815 |          2437 |               40 |              497.14 |  20110815 | 2011-08-15 00:00:00.000 | 08/15/2011    |           2 | Monday    |           15 |         227 |           34 | August      |             8 |         3 | Third         |   2011 | True        |
|            33 |         20120618 |          3826 |               40 |             2866.3  |  20120618 | 2012-06-18 00:00:00.000 | 06/18/2012    |           2 | Monday    |           18 |         170 |           25 | June        |             6 |         2 | Second        |   2012 | True        |
|            19 |         20100524 |           580 |               40 |              378    |  20100524 | 2010-05-24 00:00:00.000 | 05/24/2010    |           2 | Monday    |           24 |         144 |           22 | May         |             5 |         2 | Second        |   2010 | True        |
|            22 |         20130708 |          5520 |               15 |              175.72 |  20130708 | 2013-07-08 00:00:00.000 | 07/08/2013    |           2 | Monday    |            8 |         189 |           28 | July        |             7 |         3 | Third         |   2013 | True        |
|             7 |         20120910 |          4173 |               40 |              472.51 |  20120910 | 2012-09-10 00:00:00.000 | 09/10/2012    |           2 | Monday    |           10 |         254 |           37 | September   |             9 |         3 | Third         |   2012 | True        |
|            14 |         20120109 |          3094 |               40 |              614.06 |  20120109 | 2012-01-09 00:00:00.000 | 01/09/2012    |           2 | Monday    |            9 |           9 |            2 | January     |             1 |         1 | First         |   2012 | True        |
|             2 |         20121231 |          4665 |               40 |              589.08 |  20121231 | 2012-12-31 00:00:00.000 | 12/31/2012    |           2 | Monday    |           31 |         366 |           53 | December    |            12 |         4 | Fourth        |   2012 | True        |
|            20 |         20110815 |          2451 |               40 |              790.17 |  20110815 | 2011-08-15 00:00:00.000 | 08/15/2011    |           2 | Monday    |           15 |         227 |           34 | August      |             8 |         3 | Third         |   2011 | True        |
|            18 |         20100920 |          1072 |               16 |              142.4  |  20100920 | 2010-09-20 00:00:00.000 | 09/20/2010    |           2 | Monday    |           20 |         263 |           39 | September   |             9 |         3 | Third         |   2010 | True        |
|            14 |         20120521 |          3683 |               40 |              614.06 |  20120521 | 2012-05-21 00:00:00.000 | 05/21/2012    |           2 | Monday    |           21 |         142 |           21 | May         |             5 |         2 | Second        |   2012 | True        |
|            22 |         20120820 |          4094 |               12 |              137.38 |  20120820 | 2012-08-20 00:00:00.000 | 08/20/2012    |           2 | Monday    |           20 |         233 |           34 | August      |             8 |         3 | Third         |   2012 | True        |
|            26 |         20100802 |           876 |               11 |              110    |  20100802 | 2010-08-02 00:00:00.000 | 08/02/2010    |           2 | Monday    |            2 |         214 |           32 | August      |             8 |         3 | Third         |   2010 | True        |
|             4 |         20130204 |          4821 |               40 |              523.98 |  20130204 | 2013-02-04 00:00:00.000 | 02/04/2013    |           2 | Monday    |            4 |          35 |            6 | February    |             2 |         1 | First         |   2013 | True        |
|            28 |         20130902 |          5774 |               40 |              383.4  |  20130902 | 2013-09-02 00:00:00.000 | 09/02/2013    |           2 | Monday    |            2 |         245 |           36 | September   |             9 |         3 | Third         |   2013 | True        |
|             5 |         20100104 |             3 |               40 |              756    |  20100104 | 2010-01-04 00:00:00.000 | 01/04/2010    |           2 | Monday    |            4 |           4 |            2 | January     |             1 |         1 | First         |   2010 | True        |
|             9 |         20101220 |          1447 |               40 |              440    |  20101220 | 2010-12-20 00:00:00.000 | 12/20/2010    |           2 | Monday    |           20 |         354 |           52 | December    |            12 |         4 | Fourth        |   2010 | True        |
|            27 |         20110822 |          2488 |               40 |              776.02 |  20110822 | 2011-08-22 00:00:00.000 | 08/22/2011    |           2 | Monday    |           22 |         234 |           35 | August      |             8 |         3 | Third         |   2011 | True        |
|            30 |         20110110 |          1556 |               40 |              523.41 |  20110110 | 2011-01-10 00:00:00.000 | 01/10/2011    |           2 | Monday    |           10 |          10 |            3 | January     |             1 |         1 | First         |   2011 | True        |
|             5 |         20100607 |           625 |               40 |              756    |  20100607 | 2010-06-07 00:00:00.000 | 06/07/2010    |           2 | Monday    |            7 |         158 |           24 | June        |             6 |         2 | Second        |   2010 | True        |
|            16 |         20110404 |          1890 |               40 |              511.28 |  20110404 | 2011-04-04 00:00:00.000 | 04/04/2011    |           2 | Monday    |            4 |          94 |           15 | April       |             4 |         2 | Second        |   2011 | True        |
|            15 |         20100517 |           547 |               17 |              179.35 |  20100517 | 2010-05-17 00:00:00.000 | 05/17/2010    |           2 | Monday    |           17 |         137 |           21 | May         |             5 |         2 | Second        |   2010 | True        |



label: PayrollDateKey
DateKey
PayrollDateKey
Date
PayrollDateKey
FullDateUSA
PayrollDateKey
DayOfWeek
PayrollDateKey
DayName
PayrollDateKey
DayOfMonth
PayrollDateKey
DayOfYear
PayrollDateKey
WeekOfYear
PayrollDateKey
MonthName
PayrollDateKey
MonthOfYear
PayrollDateKey
Quarter
PayrollDateKey
QuarterName
PayrollDateKey
Year
PayrollDateKey
IsWeekday
output: {"Functional-Dependency": [["PayrollDateKey", "DateKey"], ["PayrollDateKey", "Date"], ["PayrollDateKey", "FullDateUSA"], ["PayrollDateKey", "DayOfWeek"], ["PayrollDateKey", "DayName"], ["PayrollDateKey", "DayOfMonth"], ["PayrollDateKey", "DayOfYear"], ["PayrollDateKey", "WeekOfYear"], ["PayrollDateKey", "MonthName"], ["PayrollDateKey", "MonthOfYear"], ["PayrollDateKey", "Quarter"], ["PayrollDateKey", "QuarterName"], ["PayrollDateKey", "Year"], ["PayrollDateKey", "IsWeekday"]]}
labeled_fds: PayrollDateKey
DateKey
PayrollDateKey
Date
PayrollDateKey
FullDateUSA
PayrollDateKey
DayOfWeek
PayrollDateKey
DayName
PayrollDateKey
DayOfMonth
PayrollDateKey
DayOfYear
PayrollDateKey
WeekOfYear
PayrollDateKey
MonthName
PayrollDateKey
MonthOfYear
PayrollDateKey
Quarter
PayrollDateKey
QuarterName
PayrollDateKey
Year
PayrollDateKey
IsWeekday
TimesheetTotalPay
EmployeeKey
TimesheetTotalPay
TimesheetHours
source: $MMTU_HOME/resources/Relationship-finding/FD/152859316