Boolean Functions - need help ASAP! Thanks

mred90 · **Joined:** Mon, 4 Oct 2010 20:04:01 UTC **Posts:** 3

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.

outermeasure · **Posted:** Tue, 5 Oct 2010 16:20:17 UTC

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 $xyz+\bar{x}\bar{y}z+\bar{x}y\bar{z}+x\bar{y}\bar{z}$ . Similarly ... and hence you only have free choice for F(0,0,0)

and

and so there are ... such functions.

mickyjones · **Joined:** Wed, 20 Oct 2010 12:12:48 UTC **Posts:** 2

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Boolean Functions - need help ASAP! Thanks

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