Write a function function createTable (f, n), which supplies a table for a Boolean formula ff with nn inputs, which contains the output of the formula for each input. In the program code, the function f accepts an array of Boolean values of length n as a parameter. For example, the Boolean formula a \ lor ((\ neg b) \ land c) a ((b) c) is used as a TScript function

function f (x)

{

return x [0] or ((not x [1]) and x [2]);

}

expressed.

The truth table should be returned as a nested n-dimensional array. Each individual array has two indices, where index 0 stands for false and index 1 for true. The corresponding value of the formula is stored in the innermost array. In the above example, the following three-dimensional array with a total of 8 values is expected as return (line breaks and comments only to clarify the logic):

[

[

[false, # false or ((not false) and false) = false

true], # false or ((not false) and true) = true

[false, # false or ((not true) and false) = false

false] # false or ((not true) and true) = false

],

[

[true, # true or ((not false) and false) = true

true], # true or ((not false) and true) = true

[true, # true or ((not true) and false) = true

true] # true or ((not true) and true) = true

]

]

For any values a, b, c \ in \ {0, 1 \} a, b, c {0,1} it should have the property that the call of the formula

f ([a == 1, b == 1, c == 1])

gives the same result as

createTable (f, 3) [a] [b] [c]

Hints:

You can use the last property to check the correctness of your solution.

Your solution should work for any n> 0n> 0, not just for n = 3n = 3 variables.

A recursive approach may be used to build the nested arrays.

Notice that the input to function f is an array of Boolean values, not an array of values 0 and 1. Accordingly, your function should contain the values true and false in the returned array, as is the case in the example.

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