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Old 01-09-2013, 11:28 AM
tom.mancino tom.mancino is offline
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Join Date: Jan 2013
Posts: 1
Default Re: Confused on question 6.

Originally Posted by yaser View Post
A possible target function is any function that could have generated the 5 data points in this problem, i.e., any function whose values on these five points all agree with the data.

There are 2^3=8 points in the input space here, which are all binary combinations of the 3 input variables from 000 to 111. For each of these points, a Boolean function may return 0 or 1; hence two possibilities. Therefore, for all 8 points, a Boolean function may return 2\times 2 \times \cdots \times 2 (8 times) possibilities, which gives us the number of different Boolean functions 2^{2^3}=2^8=256.
Dr. Yaser or anyone, I am a little lost still on this problem set, I think due to a fundamental lack of mathematical knowledge (i.e my fault - I am completely self taught). I am able to visualize the entire boolean set of 8 possible points (000 - 111) - i.e. the total Xn set, after a little google assistance on boolean number theory but then I get lost in attempting to understand how to compare the other Boolean functions not in X to derive the T/F values. I am assuming it is something fundamental I am missing in boolean mathematics, but am not sure.
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