Multiple choice

How many Boolean functions of three variables f (x, y, z) have the property f (x, y, z) = (f (x' , y' , z' ))?

  1. 8

  2. 16

  3. 64

  4. 256
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The condition f(x, y, z) = f(x', y', z') means the function is invariant under complementation of all inputs. There are 2^3 = 8 possible input combinations, which can be grouped into 4 pairs of (x, y, z) and (x', y', z'). For each pair, the function can take 2 values (0 or 1), leading to 2^4 = 16 possible functions.

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