Question

In: Advanced Math

Consider the relation T on the set of all undergraduate TAs (UTA) for the CSE department...

Consider the relation T on the set of all undergraduate TAs (UTA) for the CSE department where s1 T s2 if and only if s1 and s2 are UTAs for the same course.

(a) Assuming that no one is a UTA for multiple courses, prove that T is an equivalence relation.

(b) Assuming that no one is a UTA for multiple courses, what do the equivalence classes for T represent?

(c) Explain why the assumption that no one is a UTA for multiple courses is necessary for T to be an equivalence relation.

Solutions

Expert Solution

Colby Messinger answered 2 years ago
Next > < Previous

Related Solutions

Prove that isomorphism is an equivalent relation on the set of all groups.
Prove that isomorphism is an equivalent relation on the set of all groups.
Consider the following subsets of the set of all students: A = set of all science...
Consider the following subsets of the set of all students: A = set of all science majors B = set of all art majors C = set of all math majors D = set of all female students Using set operations, describe each of the following sets in terms of A, B, C, and D: a) set of all female physics majors b) set of all students majoring in both science and art
1)Let S be the set of all students at a college. Define a relation on the...
1)Let S be the set of all students at a college. Define a relation on the set S by the rule that two people are related if they live less than 2 miles apart. Is this relation an equivalence relation on S? Justify your answer. 2) Define another relation on the set S from problem 5 by defining two people as related if they have the same classification (freshman, sophomore, junior, senior or graduate student). Is this an equivalence relation...
1)Let S be the set of all students at a college. Define a relation on the...
1)Let S be the set of all students at a college. Define a relation on the set S by the rule that two people are related if they live less than 2 miles apart. Is this relation an equivalence relation on S? Justify your answer. 2) Define another relation on the set S from problem 5 by defining two people as related if they have the same classification (freshman, sophomore, junior, senior or graduate student). Is this an equivalence relation...
Suppose we define the relation R on the set of all people by the rule "a...
Suppose we define the relation R on the set of all people by the rule "a R b if and only if a is Facebook friends with b." Is this relation reflexive? Is is symmetric? Is it transitive? Is it an equivalence relation? Briefly but clearly justify your answers.
Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric, and/or...
Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric, and/or transitive, where (a, b) ∈ R if and only if a) a is taller than b. b) a and b were born on the same day.
Consider the relation R= {A, B, C, D, E, F, G, H} and the set of...
Consider the relation R= {A, B, C, D, E, F, G, H} and the set of functional dependencies: FD= {{B}—> {A}, {G}—> {D, H}, {C, H}—> {E}, {B, D}—> {F}, {D}—>{C}, {C}—> {G}} 1) Draw FD using the diagrammatic notation. 2) What are all candidate keys for R? 3) If delete {C}—>{G} and change {C, H}—> {E} to {C, H}—> {E, G}, what are all candidate keys for R
Consider the relation R defined on the set Z as follows: ∀m, n ∈ Z, (m,...
Consider the relation R defined on the set Z as follows: ∀m, n ∈ Z, (m, n) ∈ R if and only if m + n = 2k for some integer k. For example, (3, 11) is in R because 3 + 11 = 14 = 2(7). (a) Is the relation reflexive? Prove or disprove. (b) Is the relation symmetric? Prove or disprove. (c) Is the relation transitive? Prove or disprove. (d) Is it an equivalence relation? Explain.
Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric,...
Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x,y) ∈ R if and only if: a) x = 1 OR y = 1 b) x = 1 I was curious about how those two compare. I have the solutions for part a) already.
32)Of all the students applying for undergraduate studies, 13% applied to Honors college. Consider a randomly...
32)Of all the students applying for undergraduate studies, 13% applied to Honors college. Consider a randomly selected sample of 1500 students applying for undergraduate studies. Since we can view this as 1500 independent Bernoulli trials, this will be considered a binomial experiment. A)The mean of the binomial distribution is given by B)The standard deviation of this distribution is given by: C)What is the variance of this distribution? D)Find the probability that from the sample of 1500 students, strictly less than...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT