1) Structural Induction, Induction
2) Logically Valid of
3)
4)
and
5) The function f(n) :the number of perfect square numbers that < n,
f(n) is Primitive Recursive
6) The set of {m |p+q, when
Monday, November 17, 2008
Qualification Exam Theory Part
(Fall 2008 Topics)
1) Structural Induction, Induction
2) Logically Valid of![[;\forall;]](http://thewe.net/tex/%5Cforall "\forall")
and ![[;\exists;]](http://thewe.net/tex/%5Cexists "\exists")
in ![[; \exists z R(x,z) and \forall y R(x,f(x,y);]](http://thewe.net/tex/%20%5Cexists%20z%20R%28x,z%29%20and%20%5Cforall%20y%20R%28x,f%28x,y%29 "\exists z R(x,z) and \forall y R(x,f(x,y)")
3)![[; L \cap K;]](http://thewe.net/tex/%20L%20%5Ccap%20K "L \cap K")
, ![[;L \cup K;]](http://thewe.net/tex/L%20%5Ccup%20K "L \cup K")
![[; L -K ;]](http://thewe.net/tex/%20L%20-K "L -K")
: context free closure
4)![[; f: {a^nb^{f(n)} | n \in N;]](http://thewe.net/tex/%20f:%20%7Ba%5Enb%5E%7Bf%28n%29%7D%20%7C%20n%20%5Cin%20N "f: {a^nb^{f(n)} | n \in N")
is not regular
and![[;f: a^nb^{kn}| n,k \in N;]](http://thewe.net/tex/f:%20a%5Enb%5E%7Bkn%7D%7C%20n,k%20%5Cin%20N "f: a^nb^{kn}| n,k \in N")
is context free
5) The function f(n) :the number of perfect square numbers that < n,
f(n) is Primitive Recursive
6) The set of {m |p+q, when![[;p \in P;]](http://thewe.net/tex/p%20%5Cin%20P "p \in P")
and ![[; q \in Q;]](http://thewe.net/tex/%20q%20%5Cin%20Q "q \in Q")
and P and Q are recursive enumerable sets } is a recursive enumerable set.
1) Structural Induction, Induction
2) Logically Valid of
3)
4)
and
5) The function f(n) :the number of perfect square numbers that < n,
f(n) is Primitive Recursive
6) The set of {m |p+q, when
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