Question: Find the smallest relation containing the relation {(1, 2), (1, 4), (3, 3), (4, 1)} that is a) Reflexive and transitive. b) Symmetric and transitive.

Find the smallest relation containing the relation {(1, 2), (1, 4), (3, 3), (4, 1)} that is
a) Reflexive and transitive.
b) Symmetric and transitive.
c) Reflexive, symmetric, and transitive.

Step by Step Solution

★★★★★

3.36 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a We need to include at least the transitive closure which we can compute by Algorithm 1 or Al... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

923-M-C-M-S (2226).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Find the smallest equivalence relation on the set {a, b, c, d, e} containing the relation {(a, b), (a, c), (d, e)}.

Let R be a relation that is reflexive and transitive. Prove that Rn = R for all positive integers n.

Find the directed graph of the smallest relation that is both reflexive and symmetric that contains each of the relations with directed graphs shown in Exercises 5-7. In exercise 1. 2. b d

1. Find two sets A and B such that BE A and BC A. 2. Can you conclude that A =B if A, B, and C are sets such that (i) A-C B-C and (ii) A+ C = BOC 10 10 10 Give reason. 3. For the following...

1. Give a recursive definition for the sequence: 2, 4, 8, 16, 32 ? 2. Let f(x) = -2f(x-1) + 5 and f(0) = 2, find f(4). 3. In New York City, there are two non-bald people who have the same number of...

For the relation on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is symmetric, whether it is anti-symmetric, and whether it is transitive. In order to get full credits: For...

1. Let R be the relation on the set {0,1,2,3} containing the ordered pairs (0,1),(1,1),(1,2),(2, 0),(2,2), and (3,0). Find the a) reflexive closure of R. b) symmetric closure of R. 2. Find the...

Problem 2 For the problems 5a to 5c, determine whether the relation R on the set of integers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ? R if and only if a) x + y = 0....

I want to solve this question 29. Find the smallest relation containing the relation {(1,2),(1,4),(3,3),(4,1)} that is a) reflexive and transitive. b) symmetric and transitive. c) reflexive,...

Assignment (100 marks) 1) Which of the following sentences are propositions? What are the truth values of those that are propositions? (5 marks) (a) Open the door. (b) I like mathematics. (c) 2 + 4 =...

1. Explain the difficulties associated with telling businesses that its ethical responsibilities end with obedience to the law - give a current relevant business example to support your answer.

Boeing just signed a contract to sell a Boeing 737 aircraft to Air France. Air France will be billed 20.16 million payable in one year. The current spot exchange rate is $1.09/ and the one-year...

Let D be the prism in the first octan, whose base is the triangle in the x y - plane bounded by the x - axis, and the line y = x and x = 1 , whose top in the plane z = 2 - y . use triple integral in...

A model (or theory) a. is a general statement about the causal relationship between variables based on facts. b. helps explain and predict the relationship between variables. c. when expressed as a...

If f(x) = In x and g(x) = x2 9, find the functions f o g, g o f, f o f, g o g, and their domains.

Express the function F(x) =1/x + x as a composition of three functions.

Life expectancy improved dramatically in the 20th century. The table gives the life expectancy at birth (in years) of males born in the United States. Use a scatter plot to choose an appropriate type...

Bullock Prosthetics is planning to buy 3-D printing machinery costing $380,000. This machinerys expected useful life is 5 years. They require a minimum rate of return of 8%, and have calculated the...

1. Consider an artery with parameters a=D.4cm, = 40cmfs, ,u = 3 x 10'3stm2, p = lkyfm? Estimate the Reynolds number, Re, and what kind of flow, laminar or turbulent, is expected in this vessel. 2....

Question 8 Assume that the joint density function fx,y (x, y) of random variables X and Y is non-zero in the area 0 1 and y > 1. (c) So So Fxy (u, v) dudu = 1. (d) FXY (2, 2) S FXY (2, 1)