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Find whether the operations defined as f(X, Y, Z) = X'YZ + XY' + Y'Z' and g(X′, Y, Z) = X′YZ + X′YZ′ + XY functionally complete or not.

Consider the operations defined as  f(X, Y, Z) = X'YZ + XY' + Y'Z'  and  g(X′, Y, Z) = X′YZ + X′YZ′ + XY 
as we know that,
 A function is said to be complete if it can implement Complementation and OR logic / Complementation and AND logic.

  but Iam not getting how to implement on given question(i.e on function f and g)

shivani @shivani1234
28 Aug 2017 05:28 pm

F(X,Y,Z) = X'YZ + XY' +Y'Z'
G(X,Y,Z) = X'YZ + X'YZ' +XY
Lets try to prove f and g as functionally complete.
we can get NOT in f BY USING :
F(X',X,X') = XXX' + X'X' +X'X =X'
we can get OR in f BY USING :
F(X,X',Z) =X'X'Z + XX + XZ' = X'Z + X +XZ' = X'Z +X = X+Z
Thus, f is functionally complete.
Now , for g we can get NOT by using:
F(X,X',Z) = X'X'Z + X'X'Z' + XX' =X'Z +X'Z' =Z'
But we can get AND, OR so, g is not functionally complete.

Ayushi gupta @ayushivarshney
28 Aug 2017 09:39 pm

shivani for proving the function is functionally complete or not we cannot put complements. if we put complement then function is partially functionally complete.

shweta @shweta1920
28 Aug 2017 08:22 pm

@shivani1234 mere samajh nahi aaya ... pls could u elaborate procedure ? ki function f me kaise X' rakh dia x,y,z ki jagah ,

then function f me x,x',z  rakh dia ... m confused kaise kya kB kerna h