Consider the operations \(\textit{f (X, Y, Z) = X'YZ + XY' + Y'Z'}\) and…

GATE · 2015 · CS · Set 1 · Computer Science & IT

Consider the operations

f (X, Y, Z) = X’YZ + XY’ + Y’Z’\textit{f (X, Y, Z) = X'YZ + XY' + Y'Z'} and 

g (X, Y, Z) = X’YZ + X’YZ’ + XY\textit{g (X, Y, Z) = X'YZ + X'YZ' + XY}

Which one of the following is correct?

  1. A.

    Both {𝑓} and {𝑔} are functionally complete

  2. B.

    Only {𝑓} is functionally complete

  3. C.

    Only {𝑔} is functionally complete

  4. D.

    Neither {𝑓} nor {𝑔} is functionally complete

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