To simplify the given Boolean function f = A.B.C.D + A.C.D + A.D, let's apply Boolean algebra and simplify each term:

f = A.B.C.D + A.C.D + A.D

First, let's factor out the common term 'A.D' from each term:

f = A.D(B.C + C + 1)

Now, let's simplify the expression (B.C + C + 1):

B.C + C + 1 = C(B + 1) + 1 = C + 1

Substituting this back into the original expression:

f = A.D(C + 1)

Now, we can see that the simplified form of the Boolean function f is A.D.

Therefore, the correct answer is A) A.D.

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• Wrong explanation

To answer this question, we need to understand the concept of boolean functions and the number of possible combinations for 'n' boolean variables.

A boolean function is a function that takes boolean inputs and produces a boolean output. Each boolean variable can take two possible values: true (1) or false (0). Therefore, for 'n' boolean variables, there are 2^n possible combinations of input values.

For each input combination, the boolean function can produce either true or false as the output. So, for each input combination, there are 2 possible output values. Since there are 2^n possible input combinations, the total number of possible boolean functions involving 'n' boolean variables is 2^(2^n).

Now, let's go through each option to see why they are correct or incorrect:

Option A) Infinity - This option is incorrect because the number of boolean functions involving 'n' boolean variables is not infinite. It is a finite number.

Option B) n^n - This option is incorrect because n^n represents the number of possible functions mapping 'n' elements to 'n' elements, which is not the same as the number of boolean functions involving 'n' boolean variables.

Option C) n^2 - This option is incorrect because n^2 represents the number of possible functions mapping 'n' elements to 2 elements, which is also not the same as the number of boolean functions involving 'n' boolean variables.

Option D) 2^n - This option is correct because it represents the total number of possible boolean functions involving 'n' boolean variables. Each boolean variable can take 2 possible values, true or false, and there are 'n' boolean variables, resulting in 2^n possible combinations.

Therefore, the correct answer is option D) 2^n. This option is correct because it accurately represents the total number of possible boolean functions involving 'n' boolean variables.

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• Wrong explanation

To answer this question, we need to understand that the question is asking about the number of stores available in Germany.

Option A) 250 - This option is incorrect because it does not match the correct answer.

Option B) 377 - This option is correct because it matches the correct answer.

Option C) 350 - This option is incorrect because it does not match the correct answer.

Option D) 400 - This option is incorrect because it does not match the correct answer.

The correct answer is B) 377.

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• Wrong explanation