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 Post subject: Boolean Functions - need help ASAP! ThanksPosted: Tue, 5 Oct 2010 15:49:00 UTC
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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.

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 Post subject: Re: Boolean Functions - need help ASAP! ThanksPosted: Tue, 5 Oct 2010 16:20:17 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6067
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
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.

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 Post subject: Re: FoundationsPosted: Wed, 20 Oct 2010 12:39:46 UTC
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Joined: Wed, 20 Oct 2010 12:12:48 UTC
Posts: 2
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