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:
| location                         |   population_many | date                    |   HighestInfectionCount_many |   PercentagePopulationInfected_many |   population |   HighestInfectionCount |   PercentagePopulationInfected |
|:---------------------------------|------------------:|:------------------------|-----------------------------:|------------------------------------:|-------------:|------------------------:|-------------------------------:|
| Germany                          |          83783945 | 2020-08-22 00:00:00.000 |                       233861 |                         0.279124    |     83783945 |                 3736959 |                     4.46023    |
| Oceania                          |          42677809 | 2021-06-09 00:00:00.000 |                        50417 |                         0.118134    |     42677809 |                   55408 |                     0.129829   |
| Italy                            |          60461828 | 2021-06-08 00:00:00.000 |                      4235592 |                         7.0054      |     60461828 |                 4260788 |                     7.04707    |
| Tajikistan                       |           9537642 | 2021-04-23 00:00:00.000 |                        13308 |                         0.139531    |      9537642 |                   13523 |                     0.141786   |
| Sao Tome and Principe            |            219161 | 2020-05-19 00:00:00.000 |                          251 |                         0.114528    |       219161 |                    2369 |                     1.08094    |
| Romania                          |          19237682 | 2021-05-20 00:00:00.000 |                      1074297 |                         5.58434     |     19237682 |                 1080823 |                     5.61826    |
| Monaco                           |             39244 | 2021-04-24 00:00:00.000 |                         2429 |                         6.18948     |        39244 |                    2580 |                     6.57425    |
| Cameroon                         |          26545864 | 2021-06-13 00:00:00.000 |                        80090 |                         0.301704    |     26545864 |                   80858 |                     0.304597   |
| Liechtenstein                    |             38137 | 2020-10-23 00:00:00.000 |                          324 |                         0.849569    |        38137 |                    3039 |                     7.96864    |
| Sudan                            |          43849269 | 2021-06-17 00:00:00.000 |                        36347 |                         0.0828908   |     43849269 |                   36658 |                     0.0836     |
| Malta                            |            441539 | 2020-09-06 00:00:00.000 |                         2039 |                         0.461794    |       441539 |                   30627 |                     6.93642    |
| Namibia                          |           2540916 | 2021-06-27 00:00:00.000 |                        84705 |                         3.33364     |      2540916 |                   91208 |                     3.58957    |
| Burkina Faso                     |          20903278 | 2020-03-23 00:00:00.000 |                           99 |                         0.00047361  |     20903278 |                   13485 |                     0.0645114  |
| Vietnam                          |          97338583 | 2020-12-15 00:00:00.000 |                         1405 |                         0.00144342  |     97338583 |                   17727 |                     0.0182117  |
| Eswatini                         |           1160164 | 2021-04-25 00:00:00.000 |                        18442 |                         1.5896      |      1160164 |                   19084 |                     1.64494    |
| Malaysia                         |          32365998 | 2021-03-06 00:00:00.000 |                       311777 |                         0.963286    |     32365998 |                  758967 |                     2.34495    |
| Senegal                          |          16743930 | 2020-07-25 00:00:00.000 |                         9552 |                         0.0570475   |     16743930 |                   43268 |                     0.25841    |
| Azerbaijan                       |          10139175 | 2021-03-17 00:00:00.000 |                       242491 |                         2.39162     |     10139175 |                  336122 |                     3.31508    |
| Lithuania                        |           2722291 | 2021-05-22 00:00:00.000 |                       270376 |                         9.93193     |      2722291 |                  278809 |                    10.2417     |
| Brazil                           |         212559409 | 2021-02-19 00:00:00.000 |                     10084208 |                         4.74418     |    212559409 |                18622304 |                     8.76099    |
| Ecuador                          |          17643060 | 2021-06-19 00:00:00.000 |                       445586 |                         2.52556     |     17643060 |                  459538 |                     2.60464    |
| El Salvador                      |           6486201 | 2021-04-04 00:00:00.000 |                        65337 |                         1.00732     |      6486201 |                   78766 |                     1.21436    |
| China                            |        1439323774 | 2020-08-18 00:00:00.000 |                        84934 |                         0.00590097  |   1439323774 |                   91864 |                     0.00638244 |
| Comoros                          |            869595 | 2020-07-16 00:00:00.000 |                          328 |                         0.0377187   |       869595 |                    3943 |                     0.453429   |
| Monaco                           |             39244 | 2021-06-28 00:00:00.000 |                         2575 |                         6.56151     |        39244 |                    2580 |                     6.57425    |
| Bolivia                          |          11673029 | 2020-06-09 00:00:00.000 |                        14644 |                         0.125452    |     11673029 |                  441286 |                     3.78039    |
| Hungary                          |           9660350 | 2020-09-22 00:00:00.000 |                        19499 |                         0.201846    |      9660350 |                  808160 |                     8.36574    |
| Madagascar                       |          27691019 | 2021-01-01 00:00:00.000 |                        17714 |                         0.0639702   |     27691019 |                   42247 |                     0.152566   |
| Djibouti                         |            988002 | 2021-05-20 00:00:00.000 |                        11485 |                         1.16245     |       988002 |                   11602 |                     1.17429    |
| Cameroon                         |          26545864 | 2020-06-14 00:00:00.000 |                         8681 |                         0.0327019   |     26545864 |                   80858 |                     0.304597   |
| Chile                            |          19116209 | 2020-03-25 00:00:00.000 |                         1197 |                         0.0062617   |     19116209 |                 1558557 |                     8.15307    |
| Saint Vincent and the Grenadines |            110947 | 2020-08-10 00:00:00.000 |                           57 |                         0.0513759   |       110947 |                    2227 |                     2.00726    |
| Mongolia                         |           3278292 | 2020-12-05 00:00:00.000 |                          849 |                         0.0258976   |      3278292 |                  120339 |                     3.67078    |
| Ukraine                          |          43733759 | 2021-04-12 00:00:00.000 |                      1913415 |                         4.37514     |     43733759 |                 2301221 |                     5.26189    |
| Montenegro                       |            628062 | 2020-07-14 00:00:00.000 |                         1287 |                         0.204916    |       628062 |                  100272 |                    15.9653     |
| Oceania                          |          42677809 | 2020-02-18 00:00:00.000 |                           15 |                         3.51471e-05 |     42677809 |                   55408 |                     0.129829   |
| Cambodia                         |          16718971 | 2020-07-30 00:00:00.000 |                          234 |                         0.00139961  |     16718971 |                   51384 |                     0.307339   |
| Australia                        |          25499881 | 2021-03-19 00:00:00.000 |                        29192 |                         0.114479    |     25499881 |                   30684 |                     0.12033    |
| Saudi Arabia                     |          34813867 | 2020-10-08 00:00:00.000 |                       338132 |                         0.971257    |     34813867 |                  486106 |                     1.3963     |
| Jordan                           |          10203140 | 2020-12-31 00:00:00.000 |                       294494 |                         2.88631     |     10203140 |                  751937 |                     7.36966    |
| Maldives                         |            540542 | 2020-06-09 00:00:00.000 |                         1942 |                         0.359269    |       540542 |                   73931 |                    13.6772     |
| Armenia                          |           2963234 | 2020-07-11 00:00:00.000 |                        31392 |                         1.05938     |      2963234 |                  225221 |                     7.60051    |
| Gabon                            |           2225728 | 2020-09-10 00:00:00.000 |                         8621 |                         0.387334    |      2225728 |                   25054 |                     1.12565    |
| Fiji                             |            896444 | 2021-04-25 00:00:00.000 |                           91 |                         0.0101512   |       896444 |                    4849 |                     0.540915   |
| Timor                            |           1318442 | 2021-05-31 00:00:00.000 |                         6994 |                         0.530475    |      1318442 |                    9278 |                     0.703709   |
| Turkey                           |          84339067 | 2020-08-29 00:00:00.000 |                       267064 |                         0.316655    |     84339067 |                 5430940 |                     6.43941    |
| Monaco                           |             39244 | 2021-01-22 00:00:00.000 |                         1311 |                         3.34064     |        39244 |                    2580 |                     6.57425    |
| Australia                        |          25499881 | 2020-11-24 00:00:00.000 |                        27853 |                         0.109228    |     25499881 |                   30684 |                     0.12033    |
| Mali                             |          20250834 | 2020-10-05 00:00:00.000 |                         3189 |                         0.0157475   |     20250834 |                   14428 |                     0.0712464  |
| Saint Lucia                      |            183629 | 2020-08-03 00:00:00.000 |                           25 |                         0.0136144   |       183629 |                    5302 |                     2.88734    |



label: location
population
location
HighestInfectionCount
location
PercentagePopulationInfected
output: {"Functional-Dependency": [["location", "population"], ["location", "HighestInfectionCount"], ["location", "PercentagePopulationInfected"]]}
labeled_fds: location
population
location
HighestInfectionCount
location
PercentagePopulationInfected
population_many
location
population_many
HighestInfectionCount
HighestInfectionCount_many
PercentagePopulationInfected_many
PercentagePopulationInfected_many
HighestInfectionCount_many
PercentagePopulationInfected_many
PercentagePopulationInfected
population
location
population
HighestInfectionCount
HighestInfectionCount
population
HighestInfectionCount
PercentagePopulationInfected
PercentagePopulationInfected
HighestInfectionCount
source: $MMTU_HOME/resources/Relationship-finding/FD/269588538