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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?

1. EX-NOR
2. implication, negation
3. OR, negation
4. NAND

what is the meaning of  functionally complete here ??

@air1ankit  A  set is FC if you can derive all other operations from that set of operations. (Similar to universal gates).

Eg: {AND, NOT} ~ NAND, {OR, NOT} ~ NOR

@air1ankit In the answers below we know {and, not}, {or, not} and {and, or, not} are functionally complete set, therefore we are trying to derive these operations from the given operation.

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EX-NOR is not functionally complete.

NOR and NAND are functionally complete logic gates, OR , AND, NOT any logic gate can be implemented using them.

And (Implication, Negation) is also functionally complete

First complement $q$ to get $q'$ then $p \rightarrow q' = p' + q'$

Now complement the result to get AND gate $(p' + q')' \rightarrow pq$

okay bro then what we should be consider when they asked about functional complete . should it be consider partial functional complete is functional complete?
In the gate question, if they didn't use the partial functional term, then we can take external input and say it is functionally complete, otherwise they will specify in the questions.
thank u
Option -A)

B) implication,negation is functionally complete because ,

f( p , q) = p-->q = !p OR q

f( !p , q) = p OR q (since we already have NOT we can use it straightaway) .

C) is functionally complete as it is the basic functionally complete set.

D) NAND is a universal gate which can implement NOT,AND,OR . (or even anyother gates,since it is a universal gate)