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Discrete Mathematics
If A=∅
1. Is it an equivalence relation?
2. Is it antisymmetric?
1. Is it an equivalence relation?
2. Is it antisymmetric?
Discrete Mathematics
A gym coach selects to play one football team. If he can make his selection in 12,376, how many seniors are eligible to play?
Discrete Mathematics
find that the value(s) of n in each of the following
a)P(n,2)=90
b)P(n,3)=3P(n,2)
c)2P(n,2)+50=P(2n,2)
a)P(n,2)=90
b)P(n,3)=3P(n,2)
c)2P(n,2)+50=P(2n,2)
Discrete Mathematics
Which of the following problems can be solved by a standard greedy algorithm?
I. Finding a minimum spanning tree in an undirected graph with positive-integer edge weights
II. Finding a maximum clique in an undirected graph
III. Finding a maximum flow from a source node to a sink node in a directed graph with positive-integer edge
capacities
(A) I only (B) II only (C) III only (D) I and II only (E) I, II, and III
I. Finding a minimum spanning tree in an undirected graph with positive-integer edge weights
II. Finding a maximum clique in an undirected graph
III. Finding a maximum flow from a source node to a sink node in a directed graph with positive-integer edge
capacities
(A) I only (B) II only (C) III only (D) I and II only (E) I, II, and III
Discrete Mathematics
Consider the collection of all undirected graphs with 10 nodes and 6 edges. Let M and m, respectively, be the
maximum and minimum number of connected components in any graph in the collection. If a graph has no selfloops and there is at most one edge between any pair of nodes, which of the following is true?
(A) M = 10, m = 10
(B) M = 10, m = 1
(C) M = 7, m = 4
(D) M = 6, m = 4
(E) M = 6, m = 3
maximum and minimum number of connected components in any graph in the collection. If a graph has no selfloops and there is at most one edge between any pair of nodes, which of the following is true?
(A) M = 10, m = 10
(B) M = 10, m = 1
(C) M = 7, m = 4
(D) M = 6, m = 4
(E) M = 6, m = 3
Discrete Mathematics
For a connected, undirected graph G=( V, E ), which of the following must be true?
I. ∑v ∈V
degree(v) is even.
II. E ≥ |V|− 1
III. G has at least one vertex with degree 1.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
I. ∑v ∈V
degree(v) is even.
II. E ≥ |V|− 1
III. G has at least one vertex with degree 1.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Discrete Mathematics
Construct a graph based on the adjacency matrix that appears below. Label all nodes with indices consistent with the placement of numbers within the matrix.
⌈0 6 0 5 0⌉
| 6 0 1 0 3 |
| 0 1 0 4 8 |
| 5 0 4 0 0 |
⌊0 3 8 0 0⌋
•Describe the graph and why it is consistent with the matrix.
•How many simple paths are there from vertex 1 to vertex 5? Explain.Which is the shortest of those paths?
⌈0 6 0 5 0⌉
| 6 0 1 0 3 |
| 0 1 0 4 8 |
| 5 0 4 0 0 |
⌊0 3 8 0 0⌋
•Describe the graph and why it is consistent with the matrix.
•How many simple paths are there from vertex 1 to vertex 5? Explain.Which is the shortest of those paths?
Discrete Mathematics
Twenty-five different beauty products make the following claim: 13 claims for whitening the skin, 20 claims to soften the skin, 11 claims to reduce wrinkles, 8 claims to both whitening and softening the skin, 5 claims to both whitening and reducing wrinkles, and 6 claims to both softening the skin and reducing the wrinkles.
(i) Give a suitable name for the sets. Indicate the cardinality of each set. Determine and propose set operations that can be performed on the sample data above. Justify your reasons for proposing the set operations.
(ii) Create Venn diagram to represent the set operations that you derive from Question (i) above. Analyze the Venn diagram and state the conclusion that you can derive from the Venn diagram.
(iii) Analyze how many products make all three claims. Justify your answer.
(iv) Analyze how many products claim for whitening the skin but do not claim to reduce wrinkles. Justify your answer.
(v) Give another example of how sets can be applied to group objects or elements together. Support your answer by providing detailed explanation
(i) Give a suitable name for the sets. Indicate the cardinality of each set. Determine and propose set operations that can be performed on the sample data above. Justify your reasons for proposing the set operations.
(ii) Create Venn diagram to represent the set operations that you derive from Question (i) above. Analyze the Venn diagram and state the conclusion that you can derive from the Venn diagram.
(iii) Analyze how many products make all three claims. Justify your answer.
(iv) Analyze how many products claim for whitening the skin but do not claim to reduce wrinkles. Justify your answer.
(v) Give another example of how sets can be applied to group objects or elements together. Support your answer by providing detailed explanation
Discrete Mathematics
Let A ={1,2,3}
what is R if R is the relation ⊂ Ƥ (A)
How can you say that a relation is complete?
Complete is a property of relation.
please give me an example.
Thank you!
what is R if R is the relation ⊂ Ƥ (A)
How can you say that a relation is complete?
Complete is a property of relation.
please give me an example.
Thank you!
Discrete Mathematics
Let A={1,2,3}
a.) R is the relation < on A
b.) R is the relation >= on A
c. ) R is the relation ⊂ on Ƥ (A)
a.) R is the relation < on A
b.) R is the relation >= on A
c. ) R is the relation ⊂ on Ƥ (A)
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#339914 on Dec 2023
#339914 on Dec 2023