Let F be a function whose prototype is:
	bool F(int n, bool p);
such that F(n,p) can be computed in O(log n) time.
Let A be the set of unary numerals for "red" numbers, where
	a. 1 is red,
	b. if n > 1, then
		 n is red == F(n,n-1 is red)
Prove that A is in Nick's class.
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Let G be a function whose prototype is:
	int G(int n);
such that
	a.  G(n) < n/2,
	b.  it takes O(log n) time to compute G(n).
Let B = the set of binary numerals for "green" numbers, where
	c.  1 is green
	d.  If n > 1, then
		n is green == G(n) positive and green
Prove that B is polynomial.
Convince yourself that there is no easy proof that B is in Nick's class
using only the above information.
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Let H be a function whose prototype is:
	int H(int n,bool x);
such that
	a.  H(n,x) < n/2,
	b.  it takes O(log n) time to compute H(n,x)
Let C = the set of binary numerals for "blue" numbers, where
	c. 1 is blue.
        d. If n > 1, then
		n is blue == (H(n,0) is positive and blue or
		              H(n,1) is positive and blue)
Prove that C is in NP.
Convince yourself that there is no easy proof that C is polynomial
using only the above information.
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Let D be the set of binary numerals for "red" numbers, as defined above.
Prove that D is recursive.
Convince yourself that there is no easy proof that D is in NP
using only the above information.
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Let K be a function whose prototype is:
	int K(int n);
such that K(n) can be computed in O(log n) time.
Let E = the set of binary numerals for "black" numbers, where
	a.  1 is black
	b.  If n > 1, then
		n is black == K(n) is positive and black
	c.  No number is black unless it can be proved to be black
	    using the above two rules.
Prove that E is recursively enumerable.
Convince yourself that there is no easy proof that E is recursive
using only the above information.
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