Discrete Mathematics Answers

F(x)=x is one to one function true or false

13 and 65 are relatively prime? True or false

Q1 Find the floor and ceiling Function of x and . Take any value of x and y. (5)

X Floor Ceiling
-X.Y (x point y)
X / Y (x divided by y)

Q4 Write down any 4*4 matrix having only zeros and ones. (3*5=15)

a) Draw the Directed graph of that matrix.
b) List the ordered pairs in the relation on set {1, 2, 3, 4} corresponding to this matrix.
c) Determine whether the relations on this graph/ matrix are Reflexive, Symmetric and Anti-symmetric.
d) Determine whether the relation for this graph is equivalence or not?

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.