Discrete Mathematics Answers

Q3 In a prize distribution ceremony. There are first prize winner, 2nd prize winner, 3rd prize winner and fourth prize winner. Calculate the number of ways to select these winners from ___________ people who have been selected in this ceremony. (In the ___________ fill your reg no. Use the last two digits of your reg no as number of people.)

Take 5 nodes & 8 edges, Draw any Directed graph (Take help from book, but DO NOT copy paste any graph from examples or exercise.)
a) Determine whether the given graph has Hamilton circuit, if it does, find such circuit.
b) If not, provide the reason

1. State the Dijkstra’s algorithm for a directed weighted graph with all non-negative edge weights.

Let A={0,1,2}. R={(0,0),(0,1),(0,2),(1,1),(1,2),(2,2)} and S={(0,0),(1,1),(2,2)} be two relations on A. 1.Show that R is a partial order relation

2.Is R a total order relation?

3.Show that S is an equivalence relation.

A set is a fundamental building block in mathematics, and it is defined as a collection of well-defined objects.A set is always defined in a computer program with respect to an underlying universal set, and the elements in the universal set are listed in a finite order.By giving examples, discuss on how does computer representation of sets.

There are 18 mathematics majors and 325 computer science majors at a college.
a) In how many ways can two representatives be picked so that one is a mathematics major and the other is a
computer science major?
b) In how many ways can one representative be picked who is either a mathematics major or a computer science major?

If A is the set of all residents of the United states, B the set of all Canadian citizens, and C the set of all women in the world, describe the sets

A intersection B intersection B intersection C

A-B

A-C

C-A

Let A = {2,4,6} and B = {x,y,z}. State each of the following are relations from A into B.
v) R5 = {(x,2), (4,z), (2,z), (6,y)}

Let A = {2,4,6} and B = {x,y,z}. State each of the following are relations from A into B.
(iv) R4 = {(4,y), (6,x), (4,x)}

Let A = {2,4,6} and B = {x,y,z}. State each of the following are relations from A into B.
(iii) R3 = {(2,x), (4,y), (6,z)}