Path

Cycle

Degree of a vertex

Complete graph

Show, using the pigeonhole principle, that in any group of 30 people, 5 people can always be found who were born on the same day of the week.

In a tennis tournament, each entrant plays a match in the first round. Next, all winners from the first round play a second-round match. Winners continue to move on to the next round, until finally only one player is left as the tournament winner. Assuming that tournaments always involve n =  players, for some k, find the recurrence relation for the number rounds in a tournaments of n players.

A committee consisting of 2 male and2 female workers is to be constituted from 8 male and 9 female workers. In how many distinct ways can this be done ?

Define the terms Domain, Co-domain and Range in the context of a function. Also find the domain, co-domain and range for a function A to B, where A={1,2,3,4} and B={1,4,9,16,25}.

Given the Boolean expression (a  (b  c))  (b  d),draw the corresponding circuit, where a, b, c and d are the inputs to the circuitry.

Prove the following theorem by direct proof method: ‘‘The square of an even integer is an even integer.’’

What is proposition ? Explain with the help of an example. Explain Disjunction and Conjunction with the help of truth table for each.

Describe the divide-and-conquer approach to solve recurrences ? Explain how this approach can be used to apply binary search in a sorted list.

Moore and Mealy Machine.

Deterministic and Non-deterministic Turing Machine

Deterministic and Non-deterministic finite automata

What is a finite automata ? Why is it needed? How is a finite automata represented?. Also explain the term regular expression with the help of an example.

What is isomorphism? Find, if the following graphs G1 and G2 are isomorphic or not. Explain how you arrived at your answer.

Crisis counseling

Alcoholics Anonymous

Addiction and Religious Beliefs