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Discrete Mathemathics
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1. Let B {a, b} and U P(B). Draw a Hasse diagram...
10. Verify that the relations given below are quasiorders. List the elements of each equivalence class of the induced equivalence relation, and draw the Hasse (a) On the set (1,2,..., 303, define...
10. Verify that the relations given below are quasiorders. List the elements of each equivalence class of the induced equivalence relation, and draw the Hasse (a) On the set (1,2,..., 303, define mn if and only if the sum of the digits (b) On the set (1.2,3,4,11, 12, 13,14,21,22,23,24), define mn if and only diagram for the induced partial order on the equivalence classes of m is less than or equal to the sum of the digits of n. if...
1. (2 marks) Let S 2,3,4,5,6,7,8,9, 10, 11, 12). Let r be the relation on the set S defined as follows: Va,bE S, arb if and only if every prime number that divides a is a factor of b and a S b. The r...
1. (2 marks) Let S 2,3,4,5,6,7,8,9, 10, 11, 12). Let r be the relation on the set S defined as follows: Va,bE S, arb if and only if every prime number that divides a is a factor of b and a S b. The relation T is a partial order relation (you do not need to prove this). Draw the Hasse diagram for T
1. (2 marks) Let S 2,3,4,5,6,7,8,9, 10, 11, 12). Let r be the relation on the...
The drawing below shows a Hasse diagram for a partial order on the set {A, B,...
The drawing below shows a Hasse diagram for a partial order on the set {A, B, C, D, E, F, G, H, I, J} D G H E Figure 3: A Hasse diagram shows 10 vertices and 8 edges. The vertices, rep- resented by dots, are as follows: vertex J; vertices H and I are aligned vertically to the right of vertex J; vertices A, B, C, D, and E forms a closed loop, which is to the right of...
Let S = {a, b, c} and consider the poset (P(S), ⊆) where P(S) is the...
Let S = {a, b, c} and consider the poset (P(S), ⊆) where P(S) is the power set of S (set of all subsets of S). 1) Draw the Hasse Diagram of (P(S), ⊆) and draw the Hasse Diagram of a Topological Sorting of (P(S), ⊆). Thank you.
2. A binary string is a finite sequence u-діаг . . . an, where each ai is either 0 or 1. In this case n is the length o...
2. A binary string is a finite sequence u-діаг . . . an, where each ai is either 0 or 1. In this case n is the length of the string v. The strings ai, aia2,... ,ai... an-1,ai... an are all prefixes of v. On the set X of all binary strings consider the relations Ri and R2 defined as follows: Ri-(w, v) w and v have the same length ) R2 = {(u, v) I w is a prefix...
(1,3), с %3D (2,1), d (3,4) (1,2), b (4,2), f (5,3) and (5,5). Let 5. Let a = е 3 - {a, b, c, d, e, f, g} be the set of...
(1,3), с %3D (2,1), d (3,4) (1,2), b (4,2), f (5,3) and (5,5). Let 5. Let a = е 3 - {a, b, c, d, e, f, g} be the set of these 7 points. We define the following partial order on S: We have (r, y)(', y) iff x< x and y < / Draw the Hasse diagram of S S 6. We consider the same partial order as in Problem 5, but it is now defined on R2....
Q-4. [8+3+3+3+3 marks] Let be the partial order relation defined on , where means. a) Draw...
Q-4. [8+3+3+3+3 marks] Let be the partial order relation defined on , where means. a) Draw the Hasse diagram for . b) Find all maximal and minimal elements. c) Find lub({6,12}). a) Find glb({6,12}). e) What is the least element? The greatest element? Q-4. [8+3+3+3+3 marks] Let R be the partial order relation defined on A = {2,3, 6, 9, 10, 12, 14, 18, 20}, where xRy means x|y. a) Draw the Hasse diagram for R. b) Find all maximal...
3. (a Draw a diagram to represent the | (divides) partial order on the set {1,...
3. (a Draw a diagram to represent the | (divides) partial order on the set {1, 2, 3, 4, 5, 6 7,8,9, 10, (b) Identify all minimal, minimum, maximal, and maximum elements in the diagram
2. Let X be a random variable that is uniform in (1,2) U (3,5). (a) Find...
2. Let X be a random variable that is uniform in (1,2) U (3,5). (a) Find the pdf and the cdf of X. (b) Compute the expectation of X. (c) Compute the variance of X. (d) Compute the skewness of X.
please 3&4&5 3. Let S = {1,2,...,7,8) be ordered as in figure below. Consider the subset...
please 3&4&5
3. Let S = {1,2,...,7,8) be ordered as in figure below. Consider the subset A = {3,6,7} of S. a. Find the set of upper bounds of A b. Find the set of lower bounds of A C. Does sup(A) exist? d. Does inffA) exist? 4. Repeat problem 3 for the subset B = {1,2,4,7) of S. 5. Let S be the ordered set in figure below. Suppose A = {1,2,3,4,5) is order-isomorphic to S and the following...
10. Verify that the relations given below are quasiorders. List the elements of each equivalence class of the induced equivalence relation, and draw the Hasse (a) On the set (1,2,..., 303, define mn if and only if the sum of the digits (b) On the set (1.2,3,4,11, 12, 13,14,21,22,23,24), define mn if and only diagram for the induced partial order on the equivalence classes of m is less than or equal to the sum of the digits of n. if...
1. (2 marks) Let S 2,3,4,5,6,7,8,9, 10, 11, 12). Let r be the relation on the set S defined as follows: Va,bE S, arb if and only if every prime number that divides a is a factor of b and a S b. The relation T is a partial order relation (you do not need to prove this). Draw the Hasse diagram for T
1. (2 marks) Let S 2,3,4,5,6,7,8,9, 10, 11, 12). Let r be the relation on the...
The drawing below shows a Hasse diagram for a partial order on the set {A, B, C, D, E, F, G, H, I, J} D G H E Figure 3: A Hasse diagram shows 10 vertices and 8 edges. The vertices, rep- resented by dots, are as follows: vertex J; vertices H and I are aligned vertically to the right of vertex J; vertices A, B, C, D, and E forms a closed loop, which is to the right of...
2. A binary string is a finite sequence u-діаг . . . an, where each ai is either 0 or 1. In this case n is the length of the string v. The strings ai, aia2,... ,ai... an-1,ai... an are all prefixes of v. On the set X of all binary strings consider the relations Ri and R2 defined as follows: Ri-(w, v) w and v have the same length ) R2 = {(u, v) I w is a prefix...
(1,3), с %3D (2,1), d (3,4) (1,2), b (4,2), f (5,3) and (5,5). Let 5. Let a = е 3 - {a, b, c, d, e, f, g} be the set of these 7 points. We define the following partial order on S: We have (r, y)(', y) iff x< x and y < / Draw the Hasse diagram of S S 6. We consider the same partial order as in Problem 5, but it is now defined on R2....
Q-4. [8+3+3+3+3 marks] Let be the partial order relation defined on , where means. a) Draw the Hasse diagram for . b) Find all maximal and minimal elements. c) Find lub({6,12}). a) Find glb({6,12}). e) What is the least element? The greatest element? Q-4. [8+3+3+3+3 marks] Let R be the partial order relation defined on A = {2,3, 6, 9, 10, 12, 14, 18, 20}, where xRy means x|y. a) Draw the Hasse diagram for R. b) Find all maximal...
3. (a Draw a diagram to represent the | (divides) partial order on the set {1, 2, 3, 4, 5, 6 7,8,9, 10, (b) Identify all minimal, minimum, maximal, and maximum elements in the diagram
2. Let X be a random variable that is uniform in (1,2) U (3,5). (a) Find the pdf and the cdf of X. (b) Compute the expectation of X. (c) Compute the variance of X. (d) Compute the skewness of X.
please 3&4&5
3. Let S = {1,2,...,7,8) be ordered as in figure below. Consider the subset A = {3,6,7} of S. a. Find the set of upper bounds of A b. Find the set of lower bounds of A C. Does sup(A) exist? d. Does inffA) exist? 4. Repeat problem 3 for the subset B = {1,2,4,7) of S. 5. Let S be the ordered set in figure below. Suppose A = {1,2,3,4,5) is order-isomorphic to S and the following...
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