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(6 points) Let D be a digraph in which the sum of all of the outdegrees...
(6 points) Does there exist a digraph D in which no two vertices of D have...
(6 points) Does there exist a digraph D in which no two vertices of D have the same outdegree but every two vertices of D have the same indegree? If so, draw such a digraph. Otherwise, explain.
Let S = {n ∈ N | 1 ≤ n < 6} and R = {(m,...
Let S = {n ∈ N | 1 ≤ n < 6} and R = {(m, n) ∈ S × S | m ≡ n mod 3} a. List all numbers of S. b. List all ordered pairs in R. c. Does R satisfy any of the following properties: (R), (AR), (S), (AS), and/or (T)? d. Draw the digraph D presenting the relation R where S are the vertices, and R determines the directed edges. e. Give each edge in...
Please answer question 6 5. Let T2 be the digraph whose vertex set is {0,1,2}2 (i.e.,...
Please answer question 6
5. Let T2 be the digraph whose vertex set is {0,1,2}2 (i.e., n-tuples of ternary entries) and where uv is an arc iff u - v E 10,01 modulo 3. For instance, ifu 10 and v 12, then u-v 01 modulo 3 and so there is an arc uv. Determine the diameter and radius of this digraph 6, (553 students) Generalize #5 to T,., the digraph whose vertex set is [0,1,2)" and uv is an arc...
5. Let p(x) = 6 - 27r+ 39x2 – 3x - 15 (a) (2 points) How...
5. Let p(x) = 6 - 27r+ 39x2 – 3x - 15 (a) (2 points) How many zeros (real and complex, possibly with repetition) does f(x) have? What theorem did you use to get this answer? (b) (3 points) Determine all possible rational roots of p(x). (c) (2 points) What values from part (b) are actually roots of p(x)? You do not need to justify your answer. (d) (6 points) Find all other real and complex roots of p(x). Show...
1. Three 6-sided dice are tossed. Let X denote the sum of the 3 values that...
1. Three 6-sided dice are tossed. Let X denote the sum of the 3 values that occur. (a) How many ways can we have X = 3. (b) How many ways can we have X = 4. (c) How many ways can we have X = 5. (d) How many ways can all three dice give the same value? (e) How many ways can the dice give three distinct values? (f) How many ways can the first toss be the...
A digraph has 6 nodes A-F, neighbors are always kept in alpha order. DFS(A) produces a visit order of A,B,E,C,F,D while DFS(B) produces visit order B,E,C,F. Name 2 nodes that must be neighbors of nod...
A digraph has 6 nodes A-F, neighbors are always kept in alpha order. DFS(A) produces a visit order of A,B,E,C,F,D while DFS(B) produces visit order B,E,C,F. Name 2 nodes that must be neighbors of node A. (10 points) 3.
A digraph has 6 nodes A-F, neighbors are always kept in alpha order. DFS(A) produces a visit order of A,B,E,C,F,D while DFS(B) produces visit order B,E,C,F. Name 2 nodes that must be neighbors of node A. (10 points) 3.
Let A, B, C be three collinear points and let D, E, F be the midpoints...
Let A, B, C be three collinear points and let D, E, F be the midpoints of segments AB, BC, and AC, respectively. Prove that the segments DE and BF have the same midpoint. Let d be a line and let A, B, C be three points not on d. Prove that if d does not separate points A and B and it does not separate points B and C, then it does not separate points A and C.
1. Let A be a square matrix such that detal - A) = 112 - 6/11...
1. Let A be a square matrix such that detal - A) = 112 - 6/11 + 9210 a.) (3 points) What is the size of A? b.) (4 points) Is A invertible? Why or why not? c.) (3 points) How many eigenspaces does A have?
2. (5 Points) Given adjacency list representation of a digraph below with 10 vertices from 0...
2. (5 Points) Given adjacency list representation of a digraph below with 10 vertices from 0 to 9, does it have a topological order? If so, provide one. Otherwise, explain why. 0: 4 2 1 3 1: 2 2: 3 3: 4: 2 5: 1 4 3 8 9 6: 3 2 1 9 7: 2 1 8: 2 1 4 6 9: 3 1 4
5. (3, 4, 3 points) Let A-a, b, c, d, e, f, g (a) how many closed binary operations f on A satisfy Aa, b)tc b) How many closed binary operations f on A have an identity and a, b)-c? (c) How many...
5. (3, 4, 3 points) Let A-a, b, c, d, e, f, g (a) how many closed binary operations f on A satisfy Aa, b)tc b) How many closed binary operations f on A have an identity and a, b)-c? (c) How many fin (b) are commutative? 6. 10 points) Suppose that R and R are equivalent relations on the set S. Determine whether each of the following combinations of R and R2 must be an equivalent relation. (a) R1...
(6 points) Does there exist a digraph D in which no two vertices of D have the same outdegree but every two vertices of D have the same indegree? If so, draw such a digraph. Otherwise, explain.
Please answer question 6
5. Let T2 be the digraph whose vertex set is {0,1,2}2 (i.e., n-tuples of ternary entries) and where uv is an arc iff u - v E 10,01 modulo 3. For instance, ifu 10 and v 12, then u-v 01 modulo 3 and so there is an arc uv. Determine the diameter and radius of this digraph 6, (553 students) Generalize #5 to T,., the digraph whose vertex set is [0,1,2)" and uv is an arc...
5. Let p(x) = 6 - 27r+ 39x2 – 3x - 15 (a) (2 points) How many zeros (real and complex, possibly with repetition) does f(x) have? What theorem did you use to get this answer? (b) (3 points) Determine all possible rational roots of p(x). (c) (2 points) What values from part (b) are actually roots of p(x)? You do not need to justify your answer. (d) (6 points) Find all other real and complex roots of p(x). Show...
A digraph has 6 nodes A-F, neighbors are always kept in alpha order. DFS(A) produces a visit order of A,B,E,C,F,D while DFS(B) produces visit order B,E,C,F. Name 2 nodes that must be neighbors of node A. (10 points) 3.
A digraph has 6 nodes A-F, neighbors are always kept in alpha order. DFS(A) produces a visit order of A,B,E,C,F,D while DFS(B) produces visit order B,E,C,F. Name 2 nodes that must be neighbors of node A. (10 points) 3.
Let A, B, C be three collinear points and let D, E, F be the midpoints of segments AB, BC, and AC, respectively. Prove that the segments DE and BF have the same midpoint. Let d be a line and let A, B, C be three points not on d. Prove that if d does not separate points A and B and it does not separate points B and C, then it does not separate points A and C.
1. Let A be a square matrix such that detal - A) = 112 - 6/11 + 9210 a.) (3 points) What is the size of A? b.) (4 points) Is A invertible? Why or why not? c.) (3 points) How many eigenspaces does A have?
5. (3, 4, 3 points) Let A-a, b, c, d, e, f, g (a) how many closed binary operations f on A satisfy Aa, b)tc b) How many closed binary operations f on A have an identity and a, b)-c? (c) How many fin (b) are commutative? 6. 10 points) Suppose that R and R are equivalent relations on the set S. Determine whether each of the following combinations of R and R2 must be an equivalent relation. (a) R1...
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