1. (a) Define transitive relation. Give an example.

(b) Write the initial functions.

(c) Write distributive lattices.

(d) What is POSET?

(e) If A is finite set with |A|=4,determine how many binary operations can be defined on A?How many of these are commutative?

(f) Define finite set machine.

(g)  What is a partially ordered set?

2. (a) Explain various properties of relations.

(b) When do we say that a function is primitive recursive?

3. (a) If <S1,*> and <S2,*> are monoids having e1 and e2 as the respective identity elements.Prove that the direct product S1*S2 is a monoid with (e1,e2) as the identity elament.

(b) Let G be the set of all non-zero real numbers and let a*b=½ab.Show that <G,*> is an abelian group.

4. (a) Show that subset of linearly ordered poset is sublattice.

(b) Let S={a,b,c}. Draw the diagram of <P(S),>.

5. (a) Expand the function f(w,x,y,z)=w+y`z+x`y into their canonical sum-of-product.

(b)   Simplify the following expression

(a`*b`*c`)+(a*b`*c)+(a*b*c`).

6. (a) Explain homomorphism and isomorphism.

(b) Prove that a code can correct all combinations of k or fewer errors if and only if the minimum distance between the any two code words is at least 2k+1.

7. (a) Describe turing machine with suitable examples.

(b) Write deterministic finite automata for the language contains even number of zeros and even number of ones over the alphabet {0,1}.

8. (a) Write down the Hasse diagram for the positive divisors of 45.

(b) How do you equivalence FSM and sequential circuits? Explain.

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
(a) Define transitive relation. Give an example. (b) Write the initial functions. (c) Write distributive lattices. (d) What is POSET? (e) If A is finite set with |A|=4,determine how many binary operations can be defined on A?How many of these are commutative? (f) Define finite set machine. (g)  What is a partially ordered set? 2. (a)...