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The dual of a Boolean function F(x1, x2,..., xn, +, ·, ') written as FD is the same expression as that of F with + and · swapped. F is said to be self-dual if F = FD. The number of self-dual functions with Boolean variables is

1. 2ⁿ
2. 2^(n-1)
3. 2^(2ⁿ)
4. 2^(2^(n-1))

Correct answer: 2^(2^(n-1))

Solution

Self-dual functions are those that remain unchanged when the operations of AND and OR are swapped. For n Boolean variables, there are 2^(n-1) independent pairs of inputs that can determine the function's output, leading to a total of 2^(2^(n-1)) distinct self-dual functions.

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