mred90 wrote:

How many different Boolean functions F(x,y,z) are there such that

F([x],y,z) = F(x,[y],z) = F(x,y,[z])

for all values of the Boolean variables x, y, and z?

[] means the complement of (-)

I don't even understand the question.. I would understand if it asked something like "..F(x,y,z) = xy +z" .. but sadly it does not.

Just count.

Hint: Write F in full disjunctive normal form, and note conditions such as F(x,y,z)=1 implies F contains

. Similarly ... and hence you only have free choice for

and

and so there are ... such functions.