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:
| CountryRegion   | Brand                | Month     | Sale 2013   | Sale 2014   | Sale 2015   |   Budget |       x1 |       x2 |        x3 |
|:----------------|:---------------------|:----------|:------------|:------------|:------------|---------:|---------:|---------:|----------:|
| G               | Southridge Video     | October   | 5296.42     | 396.0       | 124.32      | 1375     | 20646.3  |  4599.41 |  19124.3  |
| G               | Fabrikam             | February  | 3573.93     |             | 3249.0      | 3750     | 90969.2  | 27137    | 128885    |
| C               | Wide World Importers | March     |             | 3127.7      | 3012.0      | 3750     | 48359.7  | 59935.2  |  65355.5  |
| United States   | Contoso              | September | 6232.99     | 3786.22     | 10863.67    | 7916.67  | 84152    | 40952    |  78616.9  |
| G               | A. Datum             | July      | 8778        | 1800.0      |             | 1125     | 21397    | 18774.8  |   8869.4  |
| United States   | Tailspin Toys        | July      | 258         | 280.52      | 792.87      |  708.333 |  2811.78 |  2772.85 |   3140.53 |
| C               | Proseware            | May       |             | 1749.0      |             | 1666.67  | 29281.5  | 26190.1  |  41645.8  |
| United States   | Fabrikam             | December  | 11872       |             |             | 2916.67  | 90969.2  | 27137    | 128885    |
| United States   | The Phone Company    | July      |             | 2680.0      | 1602.0      | 2083.33  | 29733    | 13890    |  21834    |
| G               | Contoso              | January   | 8172.92     | 93.78       | 6800.52     | 4166.67  | 84152    | 40952    |  78616.9  |
| United States   | Southridge Video     | May       | 4897.73     | 4841.85     | 1838.5      | 1875     | 20646.3  |  4599.41 |  19124.3  |
| United States   | Northwind Traders    | March     | 154.14      |             |             | 1250     | 13092    |   341.55 |  11201.1  |
| C               | Proseware            | August    | 1399.93     |             | 1831.5      | 1666.67  | 29281.5  | 26190.1  |  41645.8  |
| G               | Tailspin Toys        | June      |             |             | 608.0       | 1041.67  |  2811.78 |  2772.85 |   3140.53 |
| United States   | Contoso              | November  | 8218.2      | 15254.44    |             | 7916.67  | 84152    | 40952    |  78616.9  |
| C               | Fabrikam             | June      | 2820        | 28407.99    | 6223.31     | 7566.67  | 90969.2  | 27137    | 128885    |
| C               | A. Datum             | January   | ，          |             | 1935.0      |  416.667 | 21397    | 18774.8  |   8869.4  |
| United States   | Proseware            | September | 21903       | 9739.84     | 2219.0      | 2916.67  | 29281.5  | 26190.1  |  41645.8  |
| United States   | Southridge Video     | September | 1395.9      | 4718.87     | 10774.9     | 1875     | 20646.3  |  4599.41 |  19124.3  |
| G               | Contoso              | September | 13894.28    | 9406.25     | 5011.4      | 4166.67  | 84152    | 40952    |  78616.9  |
| C               | Tailspin Toys        | August    | 272.89      |             |             |  666.667 |  2811.78 |  2772.85 |   3140.53 |
| C               | Southridge Video     | November  | 1439.64     |             |             | 1875     | 20646.3  |  4599.41 |  19124.3  |
| C               | Adventure Works      | July      | 9938.12     | 2819.82     |             | 3041.67  | 56990.4  | 18042.7  |  29649.6  |
| G               | The Phone Company    | June      |             | 1400.0      |             | 2083.33  | 29733    | 13890    |  21834    |
| C               | Fabrikam             | January   | 5794.38     | 9244.97     |             | 7566.67  | 90969.2  | 27137    | 128885    |
| G               | A. Datum             | May       | 10520.5     | 3325.5      |             | 1125     | 21397    | 18774.8  |   8869.4  |
| United States   | Wide World Importers | February  | 2299        | 10971.9     |             | 4166.67  | 48359.7  | 59935.2  |  65355.5  |
| G               | Adventure Works      | May       | 3289.79     | 2583.0      | 7461.79     | 1250     | 56990.4  | 18042.7  |  29649.6  |
| C               | A. Datum             | February  | 6270        | 7059.0      |             |  416.667 | 21397    | 18774.8  |   8869.4  |
| G               | Contoso              | June      | 2743.85     | 373.52      | 3598.86     | 4166.67  | 84152    | 40952    |  78616.9  |
| United States   | Adventure Works      | November  | 4699.7      |             |             | 1300     | 56990.4  | 18042.7  |  29649.6  |
| C               | Northwind Traders    | January   | 34616.15    | 359.66      |             | 1000     | 13092    |   341.55 |  11201.1  |
| United States   | Contoso              | May       | 7133.14     | 921.35      | 7049.65     | 7916.67  | 84152    | 40952    |  78616.9  |
| G               | Northwind Traders    | February  | 5508.08     |             |             | 5416.67  | 13092    |   341.55 |  11201.1  |
| United States   | Tailspin Toys        | October   | 834.91      |             |             |  708.333 |  2811.78 |  2772.85 |   3140.53 |
| United States   | Tailspin Toys        | February  |             |             | 499.86      |  708.333 |  2811.78 |  2772.85 |   3140.53 |
| C               | Litware              | May       |             | 11186.0     | 2087.73     | 5416.67  | 74853.2  | 31861.8  | 122433    |
| C               | The Phone Company    | February  | 2408        |             |             | 2500     | 29733    | 13890    |  21834    |
| United States   | Proseware            | February  |             |             | 3669.97     | 2916.67  | 29281.5  | 26190.1  |  41645.8  |
| G               | The Phone Company    | July      |             |             | 2152.0      | 2083.33  | 29733    | 13890    |  21834    |
| G               | Northwind Traders    | December  | 18570.3     |             |             | 5416.67  | 13092    |   341.55 |  11201.1  |
| United States   | Fabrikam             | November  | 3038        | 17404.6     |             | 2916.67  | 90969.2  | 27137    | 128885    |
| United States   | Litware              | November  | 19229.82    | 9065.85     |             | 5416.67  | 74853.2  | 31861.8  | 122433    |
| C               | Adventure Works      | March     | 3689.85     | 5489.23     | 11163.94    | 3041.67  | 56990.4  | 18042.7  |  29649.6  |
| United States   | Tailspin Toys        | December  | 927.56      | 56.0        |             |  708.333 |  2811.78 |  2772.85 |   3140.53 |
| C               | Litware              | April     | 599.9       |             |             | 5416.67  | 74853.2  | 31861.8  | 122433    |
| C               | Proseware            | January   |             | 735.0       |             | 1666.67  | 29281.5  | 26190.1  |  41645.8  |
| G               | Northwind Traders    | January   | 77.07       |             |             | 5416.67  | 13092    |   341.55 |  11201.1  |
| G               | Tailspin Toys        | December  | 301         | 161.0       |             | 1041.67  |  2811.78 |  2772.85 |   3140.53 |
| G               | A. Datum             | September | 3762        | 3072.3      |             | 1125     | 21397    | 18774.8  |   8869.4  |



label: Brand
x1
Brand
x2
Brand
x3
output: {"Functional-Dependency": [["Brand", "x1"], ["Brand", "x2"], ["Brand", "x3"]]}
labeled_fds: Brand
x1
Brand
x2
Brand
x3
Sale 2013
CountryRegion
Sale 2013
Sale 2014
Sale 2013
Sale 2015
Sale 2014
CountryRegion
Sale 2014
Month
Sale 2014
Sale 2013
Sale 2014
Budget
Sale 2014
x1
Sale 2014
x2
Sale 2014
x3
Sale 2015
CountryRegion
Sale 2015
Brand
Sale 2015
Month
Sale 2015
Budget
Sale 2015
x1
Sale 2015
x2
Sale 2015
x3
source: $MMTU_HOME/resources/Relationship-finding/FD/174622366