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.