II-B.Tech. I-Semester Supplementary Examinations June 2003 DISCRETE MATHEMATICAL STRUCTURES (Computer Science and System Engineering.)
Answer any FIVE questions All questions carry equal marks --Construct the truth table for : (i) ( p V q ) p (ii) p p V q .
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1.
Max. Marks:80
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Time: 3 hours
1
Describe the clauses and clausal forms.
3.
Explain the logic programming techniques.
4.
Show that: (i) A-(A B) = A-B (ii) AB AB=B.
5.
Let N be the set of Natural numbers including zero. Determine which of the following functions are one-to-one, onto and one-to-one onto. (i) f: NN f(j) = j2 + 2 (ii) f: NN f(j) = j mod 3 1 j is odd (iii) f: NN f(j) = 0 j is even
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2.
0 j is odd
(iv) f: N 0,1 f(j) =
1 j is even
Trace the Stack contents and polish string for the infix expression a+b c-d/e h.
7.
Show that De Morgan’s laws, given by (a b)' = a' b' hold in a distributive lattice.
8.
Simplify the following Boolean expressions: (i) (a c) c [(b b') e] (ii) (1 a) (0 a' ).
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6.
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and (a b) ' = a' b'
Code No:211501
Set No.
II-B.Tech. I-Semester Supplementary Examinations June 2003 DISCRETE MATHEMATICAL STRUCTURES (Computer Science and System Engineering.)
Answer any FIVE questions All questions carry equal marks --Construct truth table for: (i) (pp) ( p p ) (ii) (pp) (p p ).
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1.
Max. Marks:80
.in
Time: 3 hours
2
Describe the Automatic Reasoning.
3.
Describe the Resolution and logic programming.
4.
Show that: (i) AB AB=A. (ii) A AB.
5.
Given S= 1,2,...,10 and a relation R on S where R= x, y / x y 10. What are the properties of relation R?
6.
Show that the intersection of any two congruence relations on a set is also congruence.
7.
Show that the lattice is distributive iff (a b) (b c) (c a) = (a b) (b c) (c a).
8.
Show that the following Boolean expressions are equal. (i) (x y) (x' z) (y z). (ii) (x y) (x' z).
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2.
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Code No:211501
Set No.
II-B.Tech. I-Semester Supplementary Examinations June 2003 DISCRETE MATHEMATICAL STRUCTURES (Computer Science and System Engineering.)
Max. Marks:80
.in
Time: 3 hours
2.
Explain substitutions and unification in predicate logic.
3.
Explain Automatic Reasoning.
4.
Describe the Pointers and link allocation.
5.
Show that the functions f and g which both are from N X N to N given by f = x+y and g < x, y>=xy are onto but not one-to-one.
6.
Define Semigroup, Semigroup homomorphism, Monoid and Monoid homomorphism.
7.
Show that lattices given by the diagrams are not distributive. 1
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1.
Answer any FIVE questions All questions carry equal marks --Construct the truth table for (p(qr)) ((pq) (pr)).
a1
a2
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a3
1
b1
b2
b3 0
0
Simplify the following Boolean expressions: (i) (a b)' (a b) '. (ii) (a' b' c) (a b' c) (a b' c').
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8.
3
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Code No:211501
Set No.
II-B.Tech. I-Semester Supplementary Examinations June 2003 DISCRETE MATHEMATICAL STRUCTURES (Computer Science and System Engineering.)
Max. Marks:80
.in
Time: 3 hours
4
2.
Explain theorem proving with Resolution.
3.
Describe logic programming techniques.
4.
What is storage structure? Describe Sequential Allocation.
5.
Show that n2 + 2n is divisible by 3.
6.
Show that the composition of two congruence relation on a set is necessarily a congruence relation.
7.
A lattice is said to be modular if a≤c a (b c) = (a b) c. Show that every distributive lattice is modular, but not conversely.
8.
Show that the following Boolean expressions are equal. (i) (x z) (x' y) (y z). (ii) (x z) (x' y).
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or ld
1.
Answer any FIVE questions All questions carry equal marks --Construct the truth table for (i) (q p ) (pq). (ii) (pq) p .
Explain the logic programming techniques. ... Describe the Resolution and logic programming. ... every distributive lattice is modular, but not conversely.
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