1.(a)   define minterms and maxterms.
(b)    construct truth table for (pvq)v  ~p.
(c)     define logical equivalence and tautology.
(d)     define rules Universal generalisation and existential generalisation.
(e)     define partial recursive funtion.
(f)      define regular funtion.
(g)      define a finite state machine.
2.(a)      show that qv(p ^ ~q)v(~p ^ ~q) is atautology.
(b)      obtain disjunctive normal form of  ~(pvq) ó(p ^q).
3. (a)        show that pv(~p ^ q)ópvq.
(b)       obtain pricipal conjunctive normal form of (~ pv ~q)-. (pó ~q).
4. (a)        show that  (x)(p(x)->p(x)) ^(x)(q(x)->r(x))=>(x)(p(x)-r(x))
(b)        verify the validity of the following argument .every living thing is a plant or animal.john’s gold fish is alive and is not a plant.all animals have hearts.therefor

5.       (a)        show that (( yp(y))-> using derivatives.
(b)         show that (x)(H(x)->A(x))->( [(y)H(y)
N(x,y)->(Y)(A(y)N(x,y))] is logically valid statement.
6. (a)          show that f(x,y)=xy  is primitive recursive function.
(b)           show that the function f(x,y)=x-y is partial recursive.
7.  (a)          let [ ] be the greatest integer   show that [.
(b)      show that the set of divisors of a positive integers is recursive.
8.  (a)      if si ≡sj then for any input sequence (six)≡(sj,x).
(b).    construct turing machine that will compute f<x,y> where f is (i) multiplication (ii)|x-y|.

tejus mahiCSE 2.2 Previous PapersCSE,CSE 2.2 Previous Papers,CSE Previous Papers,Discrete Mathematics Structures-II Previous Papers,IT,IT 2.2 Previous Papers,IT Previous Papers
1.(a)   define minterms and maxterms. (b)    construct truth table for (pvq)v  ~p. (c)     define logical equivalence and tautology. (d)     define rules Universal generalisation and existential generalisation. (e)     define partial recursive funtion. (f)      define regular funtion. (g)      define a finite state machine. 2.(a)      show that qv(p ^ ~q)v(~p ^ ~q) is atautology. (b)      obtain disjunctive normal form of ...