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Total No. of Questions : 5
Total No. of Printed Pages : 3
EW-1
M.C.A. 1st Semester (New)
Examination, 2021-22
Discrete Mathematics
Paper - MCA-101
Time : 3 Hours
[Maximum Marks : 60
Note :- Attempt all the questions. Internal choice is their in each questions. Each question carry equal marks.
Prove by mathematical induction
What are sets and its properties define partial orderedset.
OR
Give an example of a graph which is eulerian but not hamiltonian.
State and prove Lagrange's theorem on groups.
Show that every non-empty subset of a finite lattice has a least upper bound and a greatest lower bound.
What is PDA? Write the properties of PDA.
OR
What is context grammar? Give an example.
State and prove pigeonhole principle with example.
Explain deterministic and non-deterministic finite automata with example.
What is Minimum spanning tree? Explain with example.
OR
Discuss the distributive law in Lattices.
Describe various types of turing machine. Design a turing machine for the language (< (G) = anbn n ≥1}
Determine the shortest path between vertices 'a' and 'z' in graph.
Discuss Hasse diagram with suitable example.
OR
Obtain the principal conjunctive normal form and principal disjunctive normal form of (ÂŦP → R) ∧ (Q ↔ P) by using equivalences.
If U is a universal set and its two subsets A and B then prove that (A ∪ B)' = A' ∩ B'.
Define Tree? Discuss the tree traversal techniques.
Explain Chomsky normal form explain with example.
OR
Explain Kruskal's algorithm with example?
Let A = {2, 3, 4}, and B = {3, 4, 5, 6, 7} Assume a relation R from A to B such that (x, y) ∈ R when x divides y. Determine R, its domain & range.