The function below has the set of real numbers R as its domain and codomain. (a)...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The function below has the set of real numbers R as its domain and codomain. (a) If f(x) = 2x + 1 and g(y) = y 1, what is (go f)(z)? Let c P({x, y, z}) P({x, y, z}) be the function with rule c(A) = {x, y, z} A, and let n: P({x, y, z}) {0, 1, 2, 3} be the function such that n(A) is the number of elements in the set A. Which composition is defined, con or noc? For the one that is defined, described the domain and the codomain, and give an arrow diagram for the function. Consider the relation R on the set A = {0, 1, 2, 3, 4, 5, 6} with the rule that R y if x - y is divisible by 3. Draw the one-set arrow diagram for R and Ro R, and describe the latter relation with an English sentence. For each of the following functions, decide if it is one-to-one, onto, invertible, or none of these: (a) f: N N N with the rule f(a, b) = a + b. (b) f: Nx N N with the rule f(a, b) = 2. 3b. (c) f: NxN N with the rule f(a, b) = a + b. Let S = {a,b,c}, and define a function c : P(S) P(S) by c(A) = S A. (a) Is the function c one-to-one? (b) Is the function conto? (c) Is the function c is invertible, then describe the inverse of c. If c is not invertible, explain why not. Let S = {a,b,c} and let c be the function of Exercise 5. Let n : P(S) {0, 1, 2, 3} be defined so that n(X) is the number of elements in X, and let s : {0, 1,2,3} P(S) be defined by Table 4-12. (a) Which composition is defined, c o s or soc? For the one that is defined, describe the domain and the codomain, and give an arrow diagram for the function. (b) Give an arrow diagram for son. Is son one-to-one? Is son onto? (c) Give an arrow diagram for no s. Is no s one-to-one? Is nos onto? i s(i) 0 is 1 {a} Table 4-12 2 {a.b} 3 {a,b,c} Let A be the set of letters in the English alphabet. For each of the following relations on A, decide if it is reflexive, irreflexive, transitive, or antisymmetric. (Each can satisfy more than one of these properties.) (a) R = {(a, ) A A: a immediately precedes in alphabetical order} (b) R = {(a, ) A A: a comes before 3 in alphabetical order} Let A = {1,2,3}. Give an example of a relation R on A that is (a) Transitive and reflexive but not antisymmetric. (b) Antisymmetric (c) Antisymmetric and reflexive but not transitive. and transitive but not reflexive. Let S = {1,2,3}. For each of the following relations on P(S), draw the arrow diagram and decide if the relation is reflexive, antisymmetric, or transitive. If it fails any of these prop- erties, give a specific example to illustrate this. If it has all three properties (i.e., if it is a partial ordering), give the corresponding Hasse diagram. (a) R = {(A, B) = P(S) P(S): A B} (b) R = {(A,B) P(S) P(S) : B A = {3}} (c) R3 = {(A, B) = P(S) P(S): AnB = } (d) R4 = {(A, B) P(S) P(S) : An B } (e) R5 = {(A,B) = P(S) P(S) : n(A) < n(B)} The function below has the set of real numbers R as its domain and codomain. (a) If f(x) = 2x + 1 and g(y) = y 1, what is (go f)(z)? Let c P({x, y, z}) P({x, y, z}) be the function with rule c(A) = {x, y, z} A, and let n: P({x, y, z}) {0, 1, 2, 3} be the function such that n(A) is the number of elements in the set A. Which composition is defined, con or noc? For the one that is defined, described the domain and the codomain, and give an arrow diagram for the function. Consider the relation R on the set A = {0, 1, 2, 3, 4, 5, 6} with the rule that R y if x - y is divisible by 3. Draw the one-set arrow diagram for R and Ro R, and describe the latter relation with an English sentence. For each of the following functions, decide if it is one-to-one, onto, invertible, or none of these: (a) f: N N N with the rule f(a, b) = a + b. (b) f: Nx N N with the rule f(a, b) = 2. 3b. (c) f: NxN N with the rule f(a, b) = a + b. Let S = {a,b,c}, and define a function c : P(S) P(S) by c(A) = S A. (a) Is the function c one-to-one? (b) Is the function conto? (c) Is the function c is invertible, then describe the inverse of c. If c is not invertible, explain why not. Let S = {a,b,c} and let c be the function of Exercise 5. Let n : P(S) {0, 1, 2, 3} be defined so that n(X) is the number of elements in X, and let s : {0, 1,2,3} P(S) be defined by Table 4-12. (a) Which composition is defined, c o s or soc? For the one that is defined, describe the domain and the codomain, and give an arrow diagram for the function. (b) Give an arrow diagram for son. Is son one-to-one? Is son onto? (c) Give an arrow diagram for no s. Is no s one-to-one? Is nos onto? i s(i) 0 is 1 {a} Table 4-12 2 {a.b} 3 {a,b,c} Let A be the set of letters in the English alphabet. For each of the following relations on A, decide if it is reflexive, irreflexive, transitive, or antisymmetric. (Each can satisfy more than one of these properties.) (a) R = {(a, ) A A: a immediately precedes in alphabetical order} (b) R = {(a, ) A A: a comes before 3 in alphabetical order} Let A = {1,2,3}. Give an example of a relation R on A that is (a) Transitive and reflexive but not antisymmetric. (b) Antisymmetric (c) Antisymmetric and reflexive but not transitive. and transitive but not reflexive. Let S = {1,2,3}. For each of the following relations on P(S), draw the arrow diagram and decide if the relation is reflexive, antisymmetric, or transitive. If it fails any of these prop- erties, give a specific example to illustrate this. If it has all three properties (i.e., if it is a partial ordering), give the corresponding Hasse diagram. (a) R = {(A, B) = P(S) P(S): A B} (b) R = {(A,B) P(S) P(S) : B A = {3}} (c) R3 = {(A, B) = P(S) P(S): AnB = } (d) R4 = {(A, B) P(S) P(S) : An B } (e) R5 = {(A,B) = P(S) P(S) : n(A) < n(B)}
Expert Answer:
Related Book For
Discrete Mathematics and Its Applications
ISBN: 978-0073383095
7th edition
Authors: Kenneth H. Rosen
Posted Date:
Students also viewed these databases questions
-
Find an equation for the family of level surfaces corresponding to f. Describe the level surfaces. f(x, y, z) = x - y - z
-
The solid is formed by boring a conical hole into the cylinder. Determine the distance to the center of gravity. h I G Z a Z
-
An astronaut must journey to a distant planet, which is 200 light-years from Earth. What speed will be necessary if the astronaut wishes to age only 10 years during the round trip?
-
Rooter's Cleaning Services provided data concerning the costs incurred to clean hotel rooms for which hotel customers pay $150 per night. Data for the past 7 months are as follows: How much are...
-
Welch Company is considering three independent projects, each of which requires a $5 million investment. The estimated internal rate of return (IRR) and cost of capital for these projects are...
-
Given that \(f(x)=\frac{k}{2^{x}}\) is a probability distribution for a random variable that can take on the values \(x=\) \(0,1,2,3\), and 4 , find \(k\).
-
1. John Hood claims that he has no power or authority in his job. Is he correct? What sources of power work for and against him during this change process? 2. What influence tactics has Hood used...
-
Any two linearly independent functions y(x) and y2(a) that have continuous second derivatives satisfy a unique second order homogeneous linear ODE of the form Ly=y" + pi(x)y' + p2(x)y = 0.
-
Halcrow, Inc. expects to replace a downtime tracking system currently installed on CNC machines. The challenger system has a first cost of $70,000, an estimated AOC of $20,000 the first year...
-
Prudies estimate for June was slightly off. Her company actually cleaned 34 parking lots in June. For these 34 parking lots, her employees used a total of 323 gallons of detergent. This detergent...
-
A customer want to buy five items. He has only 220.0 OMR with him. The price of the products are listed: S.NO. Item Price (OMR) 1 Table 25.00 Chair 15.25 w Cupboard 32.50 Computer 25.25 Table Shoe...
-
Which is an element of applying the GAO's conceptual framework (framework)? O Apply the framework when unable to comply with the rule. O Evaluate the least restrictive rules to apply to a potential...
-
You are conducting a study testing whether a childs age is a good predictor of his or her height. You have collected the following data from a random sample of seven children: Age (months) Height...
-
Compliance strategy is one of the three strategies of - business regulation, which means setting standards for suppliers and consumers and means of assigncompliance: True or False
-
Write the output of the below given program import array as arr y=arr.array("i", y.append(25) [20,60, 70,10]) y.pop(3) y.insert (3,15) print(y[-1],y[1]) Answer:
-
Shen and Smith [Ind. Eng. Chem. Fundam., 7, 100- 105 (1968)] measured equilibrium-adsorption isotherms at four different temperatures for pure benzene vapor on silica gel, having the following...
-
Explain why each of the following is either a private good or a public good: traffic lights, in line skates, a city park, a chicken salad sandwich, a tennis racket, national defense, a coastal...
-
Describe an algorithm that determines whether a function from a finite set of integers to another finite set of integers is onto.
-
Describe a graph model that represents whether each person at a party knows the name of each other person at the party. Should the edges be directed or undirected? Should multiple edges be allowed?...
-
Draw the 4-cube Q4 and label each vertex with the minterm in the Boolean variables w, x, y, and z associated with the bit string represented by this vertex. For each literal in these variables,...
-
Reconsider the data of Problem 31. Data from Problem 31 The following three investment opportunities are available. The returns for each investment for each year vary, but the first cost of each is...
-
The following three investment opportunities are available. The returns for each investment for each year vary, but the first cost of each is $20,000. Based on a future worth analysis, which...
-
Explain the concept of a control variable and the assumption necessary for a control variable to be effective.
Study smarter with the SolutionInn App