Homework Answers
--------------------------------------
Up vote or comment. Happy Learning!
Add Answer to:
8. Let D be the set whose members are defined as follows. Basis Step: the number...
Let S be the set of binary strings defined recursively as follows: Basis step: 0ES Recursive step...
discrete math. Structural Induction: Please write and
explain clearly. Thank you.
Let S be the set of binary strings defined recursively as follows: Basis step: 0ES Recursive step: If r ES then 1rl E S and 0x0ES (I#x and y are binary strings then ry is the concatenation of and y. For instance, if 011 and y 101, then ry 011101.) (a) List the elements of S produced by te first 2 applications of the recursive definition. Find So, Si...
(10 points) Recall that the set of full binary trees is defined as follows: Basis: A...
(10 points) Recall that the set of full binary trees is defined as follows: Basis: A single vertex with no edges is a full binary tree. The root is the only vertex in the tree. Recursive rule: If T1 and T2 are full binary trees, then a new tree T' can be constructed by first placing T1 to the left of T2, adding a new vertex v at the top and then adding an edge between v and the root...
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...
7.15. Let be a finite set on which a neighborhood structure is defined; that is, each x e X has a set of neighbors N(x). Let nx be the number of neighbors of x E 2. Consider a Metropolis-Hastings alg...
7.15. Let be a finite set on which a neighborhood structure is defined; that is, each x e X has a set of neighbors N(x). Let nx be the number of neighbors of x E 2. Consider a Metropolis-Hastings algorithm with proposal density q(y x)- I/n for all y E N(x). That is, from a current state x, the proposal state is drawn from the set of neighbors with equal probability. Let the acceptance probability be Assuming the chain is...
4. (10pts) Let S be the subset of the set of binary strings defined recursively by...
4. (10pts) Let S be the subset of the set of binary strings defined recursively by Basis: XES. Recursive rule: If ze S, then c0 € S, and 1.6 ES. List the elements of S produced by the recursive definition with length less than or equal to 3.
7.15· Let X be a finite set on which a neighborhood structure is defined: that is, each x E 2 has a set of neighbors N(x). Let n be the number of neighbors of x e 2. Consider a Metropolis-Hastings al...
7.15· Let X be a finite set on which a neighborhood structure is defined: that is, each x E 2 has a set of neighbors N(x). Let n be the number of neighbors of x e 2. Consider a Metropolis-Hastings algorithm with proposal density q(y | x) l/nx for all y E N(x). That is, from a current state x, the proposal state is drawn from the set of neighbors with equal probability. Let the acceptance probability be Assuming the...
7.15. Let % be a finite set on which a neighborhood structure is defined; that is, each x E 2 has a set of neighbors N(...
7.15. Let % be a finite set on which a neighborhood structure is defined; that is, each x E 2 has a set of neighbors N(x). Let nx be the number of neighbors of x E 2. Consider a Metropolis-Hastings algorithm with proposal density q(y |x)- 1/nx for all y є N(x). That is, from a current state x, the proposal state is drawn from the set of neighbors with equal probability. Let the acceptance probability be Assuming the chain...
(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....
8. On the set A = {1,2,3,4,...,20}, an equivalence relation R is defined as follows: For...
8. On the set A = {1,2,3,4,...,20}, an equivalence relation R is defined as follows: For all x, y € A, xRy 4(x - y). For each of the following, circle TRUE or FALSE. [4 points) a. TRUE or FALSE: There are only 4 distinct equivalence classes for this relation. b. TRUE or FALSE: If you remove all the even numbers from A, the relation would still be an equivalence relation. C. TRUE or FALSE: In this equivalence relation, 2R5...
4. Let f be a differentiable function defined on (0, 1) whose derivative is f'(c) =...
4. Let f be a differentiable function defined on (0, 1) whose derivative is f'(c) = 1 - cos (+) [Note that we can confidently say such an f exists by the FTC.) Prove that f is strictly increasing on (0,1). 5. Let f be defined on [0, 1] by the following formula: 1 x = 1/n (n € N) 0, otherwise (a) Prove that f has an infinite number of discontinuities in [0,1]. (b) Prove that f is nonetheless...
discrete math. Structural Induction: Please write and
explain clearly. Thank you.
Let S be the set of binary strings defined recursively as follows: Basis step: 0ES Recursive step: If r ES then 1rl E S and 0x0ES (I#x and y are binary strings then ry is the concatenation of and y. For instance, if 011 and y 101, then ry 011101.) (a) List the elements of S produced by te first 2 applications of the recursive definition. Find So, Si...
(10 points) Recall that the set of full binary trees is defined as follows: Basis: A single vertex with no edges is a full binary tree. The root is the only vertex in the tree. Recursive rule: If T1 and T2 are full binary trees, then a new tree T' can be constructed by first placing T1 to the left of T2, adding a new vertex v at the top and then adding an edge between v and the root...
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...
7.15. Let be a finite set on which a neighborhood structure is defined; that is, each x e X has a set of neighbors N(x). Let nx be the number of neighbors of x E 2. Consider a Metropolis-Hastings algorithm with proposal density q(y x)- I/n for all y E N(x). That is, from a current state x, the proposal state is drawn from the set of neighbors with equal probability. Let the acceptance probability be Assuming the chain is...
4. (10pts) Let S be the subset of the set of binary strings defined recursively by Basis: XES. Recursive rule: If ze S, then c0 € S, and 1.6 ES. List the elements of S produced by the recursive definition with length less than or equal to 3.
7.15· Let X be a finite set on which a neighborhood structure is defined: that is, each x E 2 has a set of neighbors N(x). Let n be the number of neighbors of x e 2. Consider a Metropolis-Hastings algorithm with proposal density q(y | x) l/nx for all y E N(x). That is, from a current state x, the proposal state is drawn from the set of neighbors with equal probability. Let the acceptance probability be Assuming the...
7.15. Let % be a finite set on which a neighborhood structure is defined; that is, each x E 2 has a set of neighbors N(x). Let nx be the number of neighbors of x E 2. Consider a Metropolis-Hastings algorithm with proposal density q(y |x)- 1/nx for all y є N(x). That is, from a current state x, the proposal state is drawn from the set of neighbors with equal probability. Let the acceptance probability be Assuming the chain...
(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....
8. On the set A = {1,2,3,4,...,20}, an equivalence relation R is defined as follows: For all x, y € A, xRy 4(x - y). For each of the following, circle TRUE or FALSE. [4 points) a. TRUE or FALSE: There are only 4 distinct equivalence classes for this relation. b. TRUE or FALSE: If you remove all the even numbers from A, the relation would still be an equivalence relation. C. TRUE or FALSE: In this equivalence relation, 2R5...
4. Let f be a differentiable function defined on (0, 1) whose derivative is f'(c) = 1 - cos (+) [Note that we can confidently say such an f exists by the FTC.) Prove that f is strictly increasing on (0,1). 5. Let f be defined on [0, 1] by the following formula: 1 x = 1/n (n € N) 0, otherwise (a) Prove that f has an infinite number of discontinuities in [0,1]. (b) Prove that f is nonetheless...
Most questions answered within 3 hours.
-
A monopoly sells in two countries . The demand curves in the two
countries are p1...
asked 23 minutes ago -
A .15kg rubber ball is bounced off a wall. Before hitting the
wall, the ball moves...
asked 1 hour ago -
A manufacturing company preparing to build a new plant is
considering three potential locations for it....
asked 1 hour ago -
B. If compound Y has approximately the same values of solubility
in toluene as compound X,...
asked 1 hour ago -
Oscar Inc. has inventory in Japan valued at 39,051,000 Yen one
year ago. One year ago...
asked 1 hour ago -
If Canada suffered from "fundamental disequilibrium," and its
government choose not to devalue its currency, a...
asked 2 hours ago -
4. How many input & output Key Value Pairs are passed into,
and emitted out of...
asked 2 hours ago -
Why would your heart not function well if constructed of
skeletal muscle? What is the particular...
asked 2 hours ago -
Please respond to this essay question in full essay form for
Chemistry 1102 Organic and Biochemistry:...
asked 2 hours ago -
Determine the head loss and velocity of flow in a water supply main
of 15.0 cm...
asked 2 hours ago -
A marketing executive who knowingly authorizes a shoddy
defective product to be brought to market is...
asked 2 hours ago -
Write a psudocode:
1. Define a function called authorize that takes in 2 strings,
uName, and...
asked 2 hours ago