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Without any additional circuitry, an $8: 1 \; \mathrm{MUX}$ can be used to obtain

  1. some but not all Boolean functions of $3$ variables
  2. all functions of $3$ variables but none of $4$ variables
  3. all functions of $3$ variables and some but not all of $4$ variables
  4. all functions of $4$ variables
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