A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those. Which of the following sets of connectives is NOT functionally complete?
(B) implication, negation
(C) OR, negation
The EX-NOR is not functionally complete because we cannot synthesize all Boolean functions using EX-NOR gate only. This is primarily because we cannot obtain inverted output using EX-NOR. If we can obtain inversion from any gate then any logic function can be synthesized using that gate only.
(A.A)’ = A’+A’ = A’
OR and negation
(A+A)’ = A’.A’ = A’
Implication and negation
A->B = (A’+B)
Now if B is taken as negation of A then
A->A’ = A’+A’ = A’
Thus negation can be using these combinations of logics.
This solution is contributed by Kriti Kushwaha.
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