Thread: *ANSWER* q5
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Old 09-07-2013, 04:17 PM
GB449 GB449 is offline
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Default Re: *ANSWER* q5

Is the following solution also correct?

(iv) cannot be a growth function because for N=1, growth function according to the formula is 1. This means the number max number of dichotomies for all x is 1. Which implies for a given x the number of dichotomies is 1. Which implies for a given x, h(x) is the same for all h. Therefore for a given x & y, (h(x), h(y)) is the same for all h i.e. the cardinality of the dichotomy for any pair of values is 1 and hence the max. cardinality as we vary x & y is also 1. But substituting N = 2 in the formula gives the growth function = 2.

If the above is correct, then the same logic can be applied to determine (iii) also cannot be a growth function because, based on the formula, growth function for N=1 is 1 and for N=2, it is 2.
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