Let X = {1, 2, 3, 4, 5, 6} and let ∼ be given by {(1,...

Let X = {1, 2, 3, 4, 5, 6} and let ∼ be given by {(1, 1),(2, 2),(3, 3),(4, 4),(5, 5),(6, 6),(1, 3),(1, 5),(2, 4),(3, 1),(3, 5), (4, 2),(5, 1),(5, 3)}.

Is ∼ an equivalence relation? If yes, write down X/ ∼ .

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

6. Let A = {1, 2, 3, 4} and B = {5, 6, 7}. Let f...

6. Let A = {1, 2, 3, 4} and B = {5, 6, 7}. Let f = {(1, 5),(2, 5),(3, 6),(x, y)} where x ∈ A and y ∈ B are to be determined by you. (a) In how many ways can you pick x ∈ A and y ∈ B such that f is not a function? (b) In how many ways can you pick x ∈ A and y ∈ B such that f : A → B...

ID X Y 1 2 3 2 3 6 3 4 6 4 5 7 5...

ID X Y 1 2 3 2 3 6 3 4 6 4 5 7 5 8 7 6 5 7 7 6 7 8 8 8 9 7 8 10 12 11 Test the significance of the correlation coefficient. Then use math test scores (X) to predict physics test scores (Y). Do the following: Create a scatterplot of X and Y. Write the regression equation and interpret the regression coefficients (i.e., intercept and slope). Predict the physics score for each....

X 1 3 5 3 4 4 Y 2 5 4 3 4 6 A: Plot...

X 1 3 5 3 4 4 Y 2 5 4 3 4 6 A: Plot the date B: find the line of best fit C: determine ŷ AT x=3 D: Find r and r^2 E: explain r and r^2

1. Let R be the relation on A = {1, 2, 3, 4, 5} given by...

1. Let R be the relation on A = {1, 2, 3, 4, 5} given by R = {(1, 1),(1, 3),(2, 2),(2, 4),(2, 5),(3, 1),(3, 3),(4, 2),(4, 4),(4, 5),(5, 2),(5, 4),(5, 5)}. (a) Draw the digraph which represents R. (b) Give the 0 -1 matrix of R with respect to the natural ordering. (c) Which of the five properties (reflexive, irreflexive, symmetric, antisymmetric, transitive) does R have? Give a brief reason why or why not each property holds. 2. Let...

5. (a) Let σ = (1 2 3 4 5 6) in S6. Show that G...

5. (a) Let σ = (1 2 3 4 5 6) in S6. Show that G = {ε, σ, σ^2, σ^3, σ^4, σ^5} is a group using the operation of S6. Is G abelian? How many elements τ of G satisfy τ^2 = ε? τ^3 = ε? ε is the identity permutation. (b) Show that (1 2) is not a product of 3-cycles. Must be written as a proof! (c) If a^4 = 1 and ab = b(a^2) in a...

Given the following dataset x 1 1 2 3 4 5 y 0 2 4 5 ...

Given the following dataset x 1 1 2 3 4 5 y 0 2 4 5 5 3 We want to test the claim that there is a correlation between xand y. The level of cretaine phosphokinase (CPK) in blood samples measures the amount of muscle damage for athletes. At Jock State University, the level of CPK was determined for each of 25 football players and 15 soccer players before and after practice. The two groups of athletes are trained...

Given the following dataset x 1 1 2 3 4 5 y 0 2 4 5...

Given the following dataset x 1 1 2 3 4 5 y 0 2 4 5 5 3 We want to test the claim that there is a correlation between xand y. (a) What is the null hypothesis Ho and the alternative hypothesis H1? (b) Using α= 0.05, will you reject Ho? Justify your answer by using a p-value. (c) Base on your answer in part (b), is there evidence to support the claim? (d) Find r, the linear correlation...

2. Consider the following data: x= 1, 2, 3, 4, 5 y =3, 2, 4, 6,...

2. Consider the following data: x= 1, 2, 3, 4, 5 y =3, 2, 4, 6, 5 By hand, not using Matlab, and showing your work: (a) Compute the correlation coefficient. (b) Find the least-squares line. (c) Find the standard deviation around the least-squares line.

Let S = {1, 2, 3, 4, 5, 6, 7} be a sample of an experiment...

Let S = {1, 2, 3, 4, 5, 6, 7} be a sample of an experiment and let X = {1, 4, 7}, Y = {2, 3, 5}, and Z = {1, 3, 5} be events. Which of the following statements is correct? a) X and S are mutually exclusive events. b) X and Y are mutually exclusive events. c) X, Y, and Z are mutually exclusive events. d) Z and Y are mutually exclusive events. e) X and Z...

Maria says that 4 2/3 x 7 1/5 = 4 x 7 + 2/3 x 1/5....

Maria says that 4 2/3 x 7 1/5 = 4 x 7 + 2/3 x 1/5. Explain why Maria has made a good attempt, but her answer is not correct. Explain how to work with what Maria has already written and modify it to get the correct answer. In other words, don’t just start from scratch and show Maria how to do the problem, but rather take what she has already written, use it, and make it mathematically correct. Which...

Subjects