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                    | StockName   |      open |      high |       low |     close |   volume |      Returns |   Year |   MonthNr |   Day | Month     | Month short   |   DayInWeek | DayOfWeekName   | WeekStart               | WeekEnding              |   WeekofYear |   YearMonth |
|:------------------------|:------------|----------:|----------:|----------:|----------:|---------:|-------------:|-------:|----------:|------:|:----------|:--------------|------------:|:----------------|:------------------------|:------------------------|-------------:|------------:|
| 2019-01-24 00:00:00.000 | Amazon      | 1641.07   | 1657.26   | 1631.78   | 1654.93   |  4089943 |  0.00909135  |   2019 |         1 |    24 | January   | Jan           |           4 | Thursday        | 2019-01-21 00:00:00.000 | 2019-01-27 00:00:00.000 |            4 |      201901 |
| 2019-02-06 00:00:00.000 | Apple       |  173.237  |  174.149  |  171.455  |  172.83   | 28239591 |  0.000344387 |   2019 |         2 |     6 | February  | Feb           |           3 | Wednesday       | 2019-02-04 00:00:00.000 | 2019-02-10 00:00:00.000 |            6 |      201902 |
| 2018-03-26 00:00:00.000 | Microsoft   |   88.7773 |   92.0987 |   88.5715 |   91.8832 | 56396780 |  0.0757053   |   2018 |         3 |    26 | March     | Mar           |           1 | Monday          | 2018-03-26 00:00:00.000 | 2018-04-01 00:00:00.000 |           13 |      201803 |
| 2019-01-07 00:00:00.000 | Amazon      | 1602.31   | 1634.56   | 1589.18   | 1629.51   |  7993213 |  0.0343534   |   2019 |         1 |     7 | January   | Jan           |           1 | Monday          | 2019-01-07 00:00:00.000 | 2019-01-13 00:00:00.000 |            2 |      201901 |
| 2018-08-27 00:00:00.000 | Microsoft   |  107.938  |  108.303  |  107.187  |  108.264  | 19662331 |  0.0110695   |   2018 |         8 |    27 | August    | Aug           |           1 | Monday          | 2018-08-27 00:00:00.000 | 2018-09-02 00:00:00.000 |           35 |      201808 |
| 2018-10-03 00:00:00.000 | Facebook    |  160      |  163.66   |  159.53   |  162.43   | 23109456 |  0.0194565   |   2018 |        10 |     3 | October   | Oct           |           3 | Wednesday       | 2018-10-01 00:00:00.000 | 2018-10-07 00:00:00.000 |           40 |      201810 |
| 2018-02-05 00:00:00.000 | Facebook    |  186.93   |  190.61   |  180.61   |  181.26   | 33128206 | -0.0474038   |   2018 |         2 |     5 | February  | Feb           |           1 | Monday          | 2018-02-05 00:00:00.000 | 2018-02-11 00:00:00.000 |            6 |      201802 |
| 2019-05-16 00:00:00.000 | Apple       |  189.91   |  192.469  |  188.84   |  190.08   | 33031364 | -0.00439975  |   2019 |         5 |    16 | May       | May           |           4 | Thursday        | 2019-05-13 00:00:00.000 | 2019-05-19 00:00:00.000 |           20 |      201905 |
| 2019-05-14 00:00:00.000 | Amazon      | 1839.5    | 1852.44   | 1815.75   | 1840.12   |  4629107 |  0.00956833  |   2019 |         5 |    14 | May       | May           |           2 | Tuesday         | 2019-05-13 00:00:00.000 | 2019-05-19 00:00:00.000 |           20 |      201905 |
| 2018-03-02 00:00:00.000 | Google      | 1053.08   | 1082      | 1048.12   | 1078.92   |  2271551 |  0.00878899  |   2018 |         3 |     2 | March     | Mar           |           5 | Friday          | 2018-02-26 00:00:00.000 | 2018-03-04 00:00:00.000 |            9 |      201803 |
| 2018-09-24 00:00:00.000 | Facebook    |  161.03   |  165.7    |  160.88   |  165.41   | 19222775 |  0.0152213   |   2018 |         9 |    24 | September | Sep           |           1 | Monday          | 2018-09-24 00:00:00.000 | 2018-09-30 00:00:00.000 |           39 |      201809 |
| 2019-02-06 00:00:00.000 | Microsoft   |  106.152  |  106.152  |  104.694  |  105.19   | 20609759 | -0.011098    |   2019 |         2 |     6 | February  | Feb           |           3 | Wednesday       | 2019-02-04 00:00:00.000 | 2019-02-10 00:00:00.000 |            6 |      201902 |
| 2018-06-11 00:00:00.000 | Facebook    |  188.81   |  192.6    |  188.8    |  191.54   | 12928907 |  0.0129032   |   2018 |         6 |    11 | June      | Jun           |           1 | Monday          | 2018-06-11 00:00:00.000 | 2018-06-17 00:00:00.000 |           24 |      201806 |
| 2018-11-16 00:00:00.000 | Facebook    |  141.07   |  141.77   |  137.77   |  139.53   | 37250560 | -0.0300313   |   2018 |        11 |    16 | November  | Nov           |           5 | Friday          | 2018-11-12 00:00:00.000 | 2018-11-18 00:00:00.000 |           46 |      201811 |
| 2018-07-06 00:00:00.000 | Google      | 1123.58   | 1140.93   | 1120.74   | 1140.17   |   996079 |  0.0141425   |   2018 |         7 |     6 | July      | Jul           |           5 | Friday          | 2018-07-02 00:00:00.000 | 2018-07-08 00:00:00.000 |           27 |      201807 |
| 2019-04-16 00:00:00.000 | Facebook    |  179      |  180.17   |  178.3    |  178.87   | 11215193 | -0.00434178  |   2019 |         4 |    16 | April     | Apr           |           2 | Tuesday         | 2019-04-15 00:00:00.000 | 2019-04-21 00:00:00.000 |           16 |      201904 |
| 2018-01-30 00:00:00.000 | Amazon      | 1403.17   | 1439.25   | 1392      | 1437.82   |  5871942 |  0.0142063   |   2018 |         1 |    30 | January   | Jan           |           2 | Tuesday         | 2018-01-29 00:00:00.000 | 2018-02-04 00:00:00.000 |            5 |      201801 |
| 2019-03-11 00:00:00.000 | Facebook    |  171.6    |  174.3    |  171.58   |  172.07   | 18883983 |  0.0145637   |   2019 |         3 |    11 | March     | Mar           |           1 | Monday          | 2019-03-11 00:00:00.000 | 2019-03-17 00:00:00.000 |           11 |      201903 |
| 2018-03-16 00:00:00.000 | Amazon      | 1583.45   | 1589.44   | 1567.5    | 1571.68   |  5425012 | -0.0067243   |   2018 |         3 |    16 | March     | Mar           |           5 | Friday          | 2018-03-12 00:00:00.000 | 2018-03-18 00:00:00.000 |           11 |      201803 |
| 2018-04-06 00:00:00.000 | Apple       |  167.76   |  169.241  |  165.042  |  165.218  | 35005290 | -0.0255787   |   2018 |         4 |     6 | April     | Apr           |           5 | Friday          | 2018-04-02 00:00:00.000 | 2018-04-08 00:00:00.000 |           14 |      201804 |
| 2018-11-07 00:00:00.000 | Amazon      | 1673      | 1759.23   | 1664.08   | 1755.49   |  8192234 |  0.0685898   |   2018 |        11 |     7 | November  | Nov           |           3 | Wednesday       | 2018-11-05 00:00:00.000 | 2018-11-11 00:00:00.000 |           45 |      201811 |
| 2018-07-12 00:00:00.000 | Microsoft   |  101.128  |  102.742  |  101.088  |  102.525  | 24335929 |  0.0216711   |   2018 |         7 |    12 | July      | Jul           |           4 | Thursday        | 2018-07-09 00:00:00.000 | 2018-07-15 00:00:00.000 |           28 |      201807 |
| 2018-08-15 00:00:00.000 | Amazon      | 1909.55   | 1916.21   | 1869.79   | 1882.62   |  7700682 | -0.01929     |   2018 |         8 |    15 | August    | Aug           |           3 | Wednesday       | 2018-08-13 00:00:00.000 | 2018-08-19 00:00:00.000 |           33 |      201808 |
| 2019-02-04 00:00:00.000 | Google      | 1112.66   | 1132.8    | 1109.02   | 1132.8    |  2576470 |  0.0198515   |   2019 |         2 |     4 | February  | Feb           |           1 | Monday          | 2019-02-04 00:00:00.000 | 2019-02-10 00:00:00.000 |            6 |      201902 |
| 2018-07-30 00:00:00.000 | Facebook    |  175.3    |  175.3    |  166.56   |  171.06   | 65280787 | -0.0218995   |   2018 |         7 |    30 | July      | Jul           |           1 | Monday          | 2018-07-30 00:00:00.000 | 2018-08-05 00:00:00.000 |           31 |      201807 |
| 2018-06-19 00:00:00.000 | Amazon      | 1709.04   | 1736.11   | 1700.39   | 1734.78   |  4290117 |  0.00637549  |   2018 |         6 |    19 | June      | Jun           |           2 | Tuesday         | 2018-06-18 00:00:00.000 | 2018-06-24 00:00:00.000 |           25 |      201806 |
| 2018-04-13 00:00:00.000 | Apple       |  171.498  |  172.538  |  170.585  |  171.449  | 25124255 |  0.00338795  |   2018 |         4 |    13 | April     | Apr           |           5 | Friday          | 2018-04-09 00:00:00.000 | 2018-04-15 00:00:00.000 |           15 |      201804 |
| 2018-10-15 00:00:00.000 | Microsoft   |  107.582  |  108.145  |  105.643  |  106.288  | 32068103 | -0.0179795   |   2018 |        10 |    15 | October   | Oct           |           1 | Monday          | 2018-10-15 00:00:00.000 | 2018-10-21 00:00:00.000 |           42 |      201810 |
| 2019-05-28 00:00:00.000 | Microsoft   |  126.98   |  128      |  126.05   |  126.16   | 23128359 | -0.000633714 |   2019 |         5 |    28 | May       | May           |           2 | Tuesday         | 2019-05-27 00:00:00.000 | 2019-06-02 00:00:00.000 |           22 |      201905 |
| 2018-11-08 00:00:00.000 | Google      | 1091.38   | 1093.27   | 1072.2    | 1082.4    |  1488182 | -0.0100513   |   2018 |        11 |     8 | November  | Nov           |           4 | Thursday        | 2018-11-05 00:00:00.000 | 2018-11-11 00:00:00.000 |           45 |      201811 |
| 2018-09-10 00:00:00.000 | Microsoft   |  107.513  |  108.303  |  107.039  |  108.046  | 20727906 |  0.010812    |   2018 |         9 |    10 | September | Sep           |           1 | Monday          | 2018-09-10 00:00:00.000 | 2018-09-16 00:00:00.000 |           37 |      201809 |
| 2018-07-09 00:00:00.000 | Google      | 1148.48   | 1154.67   | 1143.42   | 1154.05   |   908969 |  0.0121736   |   2018 |         7 |     9 | July      | Jul           |           1 | Monday          | 2018-07-09 00:00:00.000 | 2018-07-15 00:00:00.000 |           28 |      201807 |
| 2018-05-24 00:00:00.000 | Microsoft   |   97.1474 |   97.359  |   95.263  |   96.7391 | 26649287 | -0.00354746  |   2018 |         5 |    24 | May       | May           |           4 | Thursday        | 2018-05-21 00:00:00.000 | 2018-05-27 00:00:00.000 |           21 |      201805 |
| 2018-08-29 00:00:00.000 | Facebook    |  176.295  |  176.79   |  174.75   |  175.9    | 18678301 | -0.00204244  |   2018 |         8 |    29 | August    | Aug           |           3 | Wednesday       | 2018-08-27 00:00:00.000 | 2018-09-02 00:00:00.000 |           35 |      201808 |
| 2018-11-29 00:00:00.000 | Microsoft   |  109.456  |  110.234  |  108.166  |  109.317  | 28123195 | -0.00836907  |   2018 |        11 |    29 | November  | Nov           |           4 | Thursday        | 2018-11-26 00:00:00.000 | 2018-12-02 00:00:00.000 |           48 |      201811 |
| 2018-06-08 00:00:00.000 | Apple       |  188.304  |  189.121  |  186.925  |  188.826  | 26656799 | -0.00909744  |   2018 |         6 |     8 | June      | Jun           |           5 | Friday          | 2018-06-04 00:00:00.000 | 2018-06-10 00:00:00.000 |           23 |      201806 |
| 2018-12-11 00:00:00.000 | Apple       |  170.271  |  170.4    |  165.649  |  167.266  | 47281665 | -0.00571903  |   2018 |        12 |    11 | December  | Dec           |           2 | Tuesday         | 2018-12-10 00:00:00.000 | 2018-12-16 00:00:00.000 |           50 |      201812 |
| 2018-02-13 00:00:00.000 | Apple       |  158.909  |  161.656  |  158.615  |  161.254  | 32549163 |  0.0100179   |   2018 |         2 |    13 | February  | Feb           |           2 | Tuesday         | 2018-02-12 00:00:00.000 | 2018-02-18 00:00:00.000 |            7 |      201802 |
| 2018-08-21 00:00:00.000 | Microsoft   |  105.616  |  106.041  |  104.559  |  104.688  | 22881861 | -0.00832741  |   2018 |         8 |    21 | August    | Aug           |           2 | Tuesday         | 2018-08-20 00:00:00.000 | 2018-08-26 00:00:00.000 |           34 |      201808 |
| 2018-04-11 00:00:00.000 | Microsoft   |   90.149  |   91.4031 |   89.6297 |   90.002  | 24872110 | -0.0109822   |   2018 |         4 |    11 | April     | Apr           |           3 | Wednesday       | 2018-04-09 00:00:00.000 | 2018-04-15 00:00:00.000 |           15 |      201804 |
| 2018-12-04 00:00:00.000 | Amazon      | 1756      | 1770.34   | 1665      | 1668.4    |  8694455 | -0.0586563   |   2018 |        12 |     4 | December  | Dec           |           2 | Tuesday         | 2018-12-03 00:00:00.000 | 2018-12-09 00:00:00.000 |           49 |      201812 |
| 2018-04-16 00:00:00.000 | Microsoft   |   92.1673 |   92.7454 |   91.5304 |   92.2653 | 20288083 |  0.0117109   |   2018 |         4 |    16 | April     | Apr           |           1 | Monday          | 2018-04-16 00:00:00.000 | 2018-04-22 00:00:00.000 |           16 |      201804 |
| 2018-11-05 00:00:00.000 | Microsoft   |  105.073  |  106.426  |  104.609  |  106.199  | 27922144 |  0.0127163   |   2018 |        11 |     5 | November  | Nov           |           1 | Monday          | 2018-11-05 00:00:00.000 | 2018-11-11 00:00:00.000 |           45 |      201811 |
| 2019-04-05 00:00:00.000 | Apple       |  195.696  |  196.344  |  195.178  |  196.244  | 18526644 |  0.00669439  |   2019 |         4 |     5 | April     | Apr           |           5 | Friday          | 2019-04-01 00:00:00.000 | 2019-04-07 00:00:00.000 |           14 |      201904 |
| 2019-03-11 00:00:00.000 | Apple       |  174.817  |  178.433  |  174.677  |  178.214  | 32011034 |  0.0346422   |   2019 |         3 |    11 | March     | Mar           |           1 | Monday          | 2019-03-11 00:00:00.000 | 2019-03-17 00:00:00.000 |           11 |      201903 |
| 2018-06-18 00:00:00.000 | Apple       |  185.063  |  186.383  |  184.393  |  185.91   | 18484865 | -0.000529546 |   2018 |         6 |    18 | June      | Jun           |           1 | Monday          | 2018-06-18 00:00:00.000 | 2018-06-24 00:00:00.000 |           25 |      201806 |
| 2018-07-02 00:00:00.000 | Facebook    |  193.37   |  197.45   |  192.22   |  197.36   | 13961578 |  0.0156443   |   2018 |         7 |     2 | July      | Jul           |           1 | Monday          | 2018-07-02 00:00:00.000 | 2018-07-08 00:00:00.000 |           27 |      201807 |
| 2019-04-12 00:00:00.000 | Amazon      | 1848.4    | 1851.5    | 1841.3    | 1843.06   |  3114413 | -0.000547702 |   2019 |         4 |    12 | April     | Apr           |           5 | Friday          | 2019-04-08 00:00:00.000 | 2019-04-14 00:00:00.000 |           15 |      201904 |
| 2018-02-09 00:00:00.000 | Facebook    |  174.76   |  176.9    |  167.18   |  176.11   | 39887626 |  0.0264017   |   2018 |         2 |     9 | February  | Feb           |           5 | Friday          | 2018-02-05 00:00:00.000 | 2018-02-11 00:00:00.000 |            6 |      201802 |
| 2018-07-31 00:00:00.000 | Google      | 1220.01   | 1227.59   | 1205.6    | 1217.26   |  1644722 | -0.00203322  |   2018 |         7 |    31 | July      | Jul           |           2 | Tuesday         | 2018-07-30 00:00:00.000 | 2018-08-05 00:00:00.000 |           31 |      201807 |



label: Date
Year
Date
MonthNr
Date
Day
Date
Month
Date
Month short
Date
DayInWeek
Date
DayOfWeekName
Date
WeekStart
Date
WeekEnding
Date
WeekofYear
Date
YearMonth
output: {"Functional-Dependency": [["Date", "Year"], ["Date", "MonthNr"], ["Date", "Day"], ["Date", "Month"], ["Date", "Month short"], ["Date", "DayInWeek"], ["Date", "DayOfWeekName"], ["Date", "WeekStart"], ["Date", "WeekEnding"], ["Date", "WeekofYear"], ["Date", "YearMonth"]]}
labeled_fds: Date
Year
Date
MonthNr
Date
Day
Date
Month
Date
Month short
Date
DayInWeek
Date
DayOfWeekName
Date
WeekStart
Date
WeekEnding
Date
WeekofYear
Date
YearMonth
open
Date
open
StockName
open
high
open
low
open
close
open
volume
open
Returns
open
Year
open
MonthNr
open
Day
open
Month
open
Month short
open
DayInWeek
open
DayOfWeekName
open
WeekStart
open
WeekEnding
open
WeekofYear
open
YearMonth
high
StockName
high
open
high
low
high
close
high
Returns
high
Year
high
MonthNr
high
Day
high
Month
high
Month short
high
DayInWeek
high
DayOfWeekName
high
WeekStart
high
WeekEnding
high
WeekofYear
high
YearMonth
low
StockName
low
open
low
volume
low
Year
low
MonthNr
low
Day
low
Month
low
Month short
low
DayInWeek
low
DayOfWeekName
low
WeekStart
low
WeekEnding
low
WeekofYear
low
YearMonth
close
Date
close
StockName
close
open
close
high
close
low
close
volume
close
Returns
close
Year
close
MonthNr
close
Month
close
Month short
close
DayInWeek
close
DayOfWeekName
close
WeekStart
close
WeekEnding
close
WeekofYear
close
YearMonth
Returns
Date
Returns
StockName
Returns
open
Returns
high
Returns
low
Returns
close
Returns
volume
Returns
MonthNr
Returns
Day
Returns
Month
Returns
Month short
Returns
DayInWeek
Returns
DayOfWeekName
Returns
WeekStart
Returns
WeekEnding
Returns
WeekofYear
Returns
YearMonth
WeekStart
Year
WeekStart
WeekofYear
WeekEnding
Year
WeekEnding
WeekofYear
source: $MMTU_HOME/resources/Relationship-finding/FD/125640537