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Discrete Mathematics
How many bit strings of length 8 either start with 1 bit or end with 2 bits 0
Discrete Mathematics
Consider following relation on set (1, 2, 3, 4, 5, 6}
R= {(i,j) | |i-j|=2}
Is R transitive?
Is R reflexive?
Is R symmetric?
R= {(i,j) | |i-j|=2}
Is R transitive?
Is R reflexive?
Is R symmetric?
Discrete Mathematics
Given set S = {1, 2, 3, 4, 5, 6} and a partition of S,
A1 = {1, 2, 3}
A2 = {4, 5}
A3 = {6}
Find the ordered pairs that make up the equivalence relation R produced by that
partition
A1 = {1, 2, 3}
A2 = {4, 5}
A3 = {6}
Find the ordered pairs that make up the equivalence relation R produced by that
partition
Discrete Mathematics
Let R be the relation on the set A = {a, b, c, d, e, f} and
R = {(a,c), (b,d), (c,a), (c,e), (d,b), (d,f), (e,c), (f,d)}
Find the transitive closure pf R using Warshall’s algorithm.
R = {(a,c), (b,d), (c,a), (c,e), (d,b), (d,f), (e,c), (f,d)}
Find the transitive closure pf R using Warshall’s algorithm.
Discrete Mathematics
Construct the Hasse diagram for ({1, 2, 3}, <=)
Discrete Mathematics
A. Give a summary of the Greedy Algorithm.
B. Give a summary of the Edge-Picking Algorithm.
C. What is a graph coloring, and how is it applied?
B. Give a summary of the Edge-Picking Algorithm.
C. What is a graph coloring, and how is it applied?
Discrete Mathematics
Eulerian and Hamiltonian Graphs, Weighted Graphs
A. Define the following:
1. Walk
2. Path, Trail
3. Cycle, Circuit
B. What is Eulerian Graph?
C. What is Hamiltonian Graph?
D. Describe how to solve the Konigsberg Problem.
A. Define the following:
1. Walk
2. Path, Trail
3. Cycle, Circuit
B. What is Eulerian Graph?
C. What is Hamiltonian Graph?
D. Describe how to solve the Konigsberg Problem.
Discrete Mathematics
A. Give a brief definition of the following:
1. Graph
2. Degree of a vertex
3. Isomorphic graphs
B. Give 4 types of graphs and give a brief description (you may describe in words or just draw a sample graph).
1. Graph
2. Degree of a vertex
3. Isomorphic graphs
B. Give 4 types of graphs and give a brief description (you may describe in words or just draw a sample graph).
Discrete Mathematics
Prove or disprove: every transitive relation on a set X with more 2 points is reflexive
Discrete Mathematics
1) Let P, Q, and R be the propositions
P : Grizzly bears have been seen in the area.
Q : Hiking is safe on the trail.
R : Berries are ripe along the trail.
Write these propositions using p, q, and r and logical connectives (including
negations).
a) Berries are ripe along the trail, but grizzly bears have not been seen in the
area.
b) Grizzly bears have not been seen in the area and hiking on the trail is safe,
but berries are ripe along the trail.
c) If berries are ripe along the trail, hiking is safe if and only if grizzly bears
have not been seen in the area.
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#340153 on Dec 2023
#340153 on Dec 2023