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The functionally complete set is

  • A.{ ^, v }
  • B.{↓, ^ }
  • C.{↑}
  • D.Both (b) and (c)

Answer: D

Correct answer: Both (b) and (c)

A set is functionally complete if every truth function can be expressed with it. NOR alone will do, since \( \lnot p \) is \( p \downarrow p \) and the rest follows, so the second set is complete; and NAND alone is complete for the same reason, which is why a whole processor can be built from NAND gates. The set with only conjunction and disjunction cannot express negation and so is not complete.

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