Question 2 (10%) (a) Draw a poset diagram for the poset P = { φ ,...
Question 2 (10%)
(a) Draw a poset diagram for the poset P = { φ , { a } , { b } , { c } , { a, b } , { a, c } , { b, c } , { a, b, c }} , with the subset relation.
(b) Describe the glb and lub of pairs of elements in terms of set operations. That is, given two elements S and T in the above poset, what is the glb of S and T ? What is the lub of S and T ? Hint: S ∪ T is the lub of S and T
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Question 2 (10%)
(a) Draw a poset diagram for the poset P = { φ ,...
Partial-ordered relation
Given a partial - ordered relation {(a, b) a bisects b} on the set {2, 4, 6, 8, 10, 60, 120, 240). a. Draw a Hasse diagram of poset b. Look for the maximum element. c. Look for the minimal elements. d. If so, look for the greatest element - in the poset? e. If so, look for the smallest element in the poset? f. Find UB from (30, 60) g. Find the LB of (30, 60) h. Find LUB...
QUESTION 7 Consider the poset (A, R) represented by the following Hasse diagram (2 (a) Give each of the following If any do not exıst, explan why (i) The greatest element of (A, R) (i:) The least ele...
QUESTION 7 Consider the poset (A, R) represented by the following Hasse diagram (2 (a) Give each of the following If any do not exıst, explan why (i) The greatest element of (A, R) (i:) The least element of (A, R) (i) All upper bounds of {h, eh (iv) The least upper bound (LUB) or(h (v) All lower bounds of (b,c) (vi) The greatest lower bound (GLB) or(b, c} (b) Give complete reasons for the answers to the following (i)...
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.
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...
Consider the poset S = ({P{1,2,3} - {0}), S) (a) List any minimal elements (b) If...
Consider the poset S = ({P{1,2,3} - {0}), S) (a) List any minimal elements (b) If it exists give the minimum element (c) List any maximal elements (d) If it exists give the maximum element (e) Give the Hasse diagram for S
Show your work, please 4. Partial Orders Let P be the collection of all subsets of...
Show your work, please
4. Partial Orders Let P be the collection of all subsets of X = {a,b,c,d} that have at least two elements. (So {a,c} € P, but {b} P.) Consider the subset relation C as a partial order on P. For example, {a,b} = {a,b,c}. Draw the Hasse diagram, and find any maximum/minimum elements, and maximal/minimal elements.
8. Let S = {1, 2, 3, 4). With respect to the lexicographic order based on...
8. Let S = {1, 2, 3, 4). With respect to the lexicographic order based on the usual less than relation, (a) find all pairs in S x S less than (2,3) (b) find all pairs in Sx S greater than (3, 1) (c) draw the Hasse diagram of the poset (SxS,
2 In the block diagram below, G(s) -1/s, P(s)P(s) s-+2 s+2 D(s)- k-oo Ше-ks[1-e-s/1001. The inver...
2 In the block diagram below, G(s) -1/s, P(s)P(s) s-+2 s+2 D(s)- k-oo Ше-ks[1-e-s/1001. The inverse Laplace transforms of these equations are g(t), p(t),p(t), and d(t), respectively. The parameter K scales the feedback k-0 D(s) R(s) G(s) P(s) C(s) P(s) A Consider for a moment, D(s)- 0. Simplify the block diagram in terms of G(s), P(s), P(s) and find the transfer function by substituting the equations given above B What are the zeros and poles of the system you obtained...
5. (a) Write out the set P({a, 2,0}). (b) For sets A, B and C, draw...
5. (a) Write out the set P({a, 2,0}). (b) For sets A, B and C, draw the Venn diagram representing AU( B C), (c) For sets A, B and C, draw the Venn diagram representing (AUD) n(B\C). (d) If A and B are two boxes (possibly with things inside), describe the following in terms of boxes A B, P(A), and A.
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...
QUESTION 7 Consider the poset (A, R) represented by the following Hasse diagram (2 (a) Give each of the following If any do not exıst, explan why (i) The greatest element of (A, R) (i:) The least element of (A, R) (i) All upper bounds of {h, eh (iv) The least upper bound (LUB) or(h (v) All lower bounds of (b,c) (vi) The greatest lower bound (GLB) or(b, c} (b) Give complete reasons for the answers to the following (i)...
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...
Consider the poset S = ({P{1,2,3} - {0}), S) (a) List any minimal elements (b) If it exists give the minimum element (c) List any maximal elements (d) If it exists give the maximum element (e) Give the Hasse diagram for S
Show your work, please
4. Partial Orders Let P be the collection of all subsets of X = {a,b,c,d} that have at least two elements. (So {a,c} € P, but {b} P.) Consider the subset relation C as a partial order on P. For example, {a,b} = {a,b,c}. Draw the Hasse diagram, and find any maximum/minimum elements, and maximal/minimal elements.
8. Let S = {1, 2, 3, 4). With respect to the lexicographic order based on the usual less than relation, (a) find all pairs in S x S less than (2,3) (b) find all pairs in Sx S greater than (3, 1) (c) draw the Hasse diagram of the poset (SxS,
2 In the block diagram below, G(s) -1/s, P(s)P(s) s-+2 s+2 D(s)- k-oo Ше-ks[1-e-s/1001. The inverse Laplace transforms of these equations are g(t), p(t),p(t), and d(t), respectively. The parameter K scales the feedback k-0 D(s) R(s) G(s) P(s) C(s) P(s) A Consider for a moment, D(s)- 0. Simplify the block diagram in terms of G(s), P(s), P(s) and find the transfer function by substituting the equations given above B What are the zeros and poles of the system you obtained...
5. (a) Write out the set P({a, 2,0}). (b) For sets A, B and C, draw the Venn diagram representing AU( B C), (c) For sets A, B and C, draw the Venn diagram representing (AUD) n(B\C). (d) If A and B are two boxes (possibly with things inside), describe the following in terms of boxes A B, P(A), and A.
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...
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