JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD MCA 1 MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE Previous Question Paper (October/November - 2022 - R20)

Construct a truth table for each of these compound propositions:

i) (P ↔ q) ⊕ (p ↔ ¬q)

ii) (p ⊕ q) → (p ⊕ ¬q)

State the converse, contrapositive and inverse of each of these conditional statements:

i) If it snows tonight, then I will stay at home.

ii) I go to the beach whenever it is a sunny summer day.

What do you mean by a logical equivalence? Give identity, idempotent, commutative, associative, distributive and De Morgan’s laws of Boolean algebra.

Use of rules of inference to show that ∀x (P(x) → (Q(x) ∧ S(x))) and ∀x(P(x) ∧ R(x)) are true, then ∀x (R(x) ∧ S(x)) is true.

Let A = {a, b, c}, B = {x, y}, and C = {0, 1}. Find A × B × C and C × B × A.

Let A, B, and C be sets. Show that

Give examples of different types of correspondences.

Find a8 of the sequence {an} if an equals

Determine whether relation R = [[1, 1, 1], [0, 1, 1], [1, 1, 1]] is an equivalence relation or not.

Demonstrate with an example bubble sort algorithm.

Explain big-omega and big-theta notations with examples.

Prove that the sum of first n positive odd integers is

Give a recursive definition of the set of positive integers that are multiples of 5.

Explain the following:

i) Conditional probability

ii) Independence of events

What is the Tower of Hanoi problem? Let Hn denote the number of moves needed to solve the Tower of Hanoi problem with n disks. Give a recurrence relation for the sequence {Hn}.

What are complete and planar graphs? Is K4 a planar graph? If so give non-planar embedding of K4.

Give the order of vertices visited in pre-order, in-order and post-order traversal of the following tree.