# Andhra University BE/B.Tech Discrete Mathematics Structures-II Previous Paper 2010

- (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 <S_{1},*> and <S_{2},*> are monoids having e_{1} and e_{2} as the respective identity elements.Prove that the direct product S_{1}*S_{2} is a monoid with (e_{1},e_{2}) 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.

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