10. Which of the following Boolean functions is algebraically complete?

  1. F = xy
  2. F = x + y
  3. F = x'
  4. F = xy + yz
  5. F = x + y'

5 is CORRECT. F is algebraically complete implies that combinations of F functions can produce the AND, OR and NOT functions. F(x, y) = x + y' can do this because it has a NOT and a OR in it; DeMorgan's theorem can produce the missing AND. Here is how F can generate all three fundamental operations:
NOT: F(0, B) = B'
OR: F(A, F(0, B)) = A + B
AND: F(0, F(F(0, A), B)) = A*B (DeMorgan's theorem applied to get the AND = *)

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