Question

Let A = {1, 2, 3, 4, 5}. Describe an equivalence relation R on the set...

Let A = {1, 2, 3, 4, 5}. Describe an equivalence relation R on the set A that produces the following partition (has the sets of the partition as its equivalence classes): A1 = {1, 4}, A2 = {2, 5}, A3 = {3} You are free to describe R as a set, as a directed graph, or as a zero-one matrix.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Answer: R = { (x,y) is in A×A : 3 | (x-y) }

Feel free to ask any doubt in comment section. Thank you. ?

Please give an upvote if you liked my answer. It will be highly encouraging for me. Thank you.?

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let A = {−5, −4, −3, −2, −1, 0, 1, 2, 3} and define a relation...
Let A = {−5, −4, −3, −2, −1, 0, 1, 2, 3} and define a relation R on A as follows: For all (m, n) is in A, m R n ⇔ 5|(m2 − n2). It is a fact that R is an equivalence relation on A. Use set-roster notation to list the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.) ____________
Let A be a non-empty set. Prove that if ∼ defines an equivalence relation on the...
Let A be a non-empty set. Prove that if ∼ defines an equivalence relation on the set A, then the set of equivalence classes of ∼ form a partition of A.
Determine the distance equivalence classes for the relation R is defined on ℤ by a R...
Determine the distance equivalence classes for the relation R is defined on ℤ by a R b if |a - 2| = |b - 2|. I had to prove it was an equivalence relation as well, but that part was not hard. Just want to know if the logic and presentation is sound for the last part: 8.48) A relation R is defined on ℤ by a R b if |a - 2| = |b - 2|. Prove that R...
For each of the following, prove that the relation is an equivalence relation. Then give the...
For each of the following, prove that the relation is an equivalence relation. Then give the information about the equivalence classes, as specified. a) The relation ∼ on R defined by x ∼ y iff x = y or xy = 2. Explicitly find the equivalence classes [2], [3], [−4/5 ], and [0] b) The relation ∼ on R+ × R+ defined by (x, y) ∼ (u, v) iff x2v = u2y. Explicitly find the equivalence classes [(5, 2)] and...
1. a. Consider the definition of relation. If A is the set of even numbers and...
1. a. Consider the definition of relation. If A is the set of even numbers and ≡ is the subset of ordered pairs (a,b) where a<b in the usual sense, is ≡ a relation? Explain. b. Consider the definition of partition on the bottom of page 18. Theorem 2 says that the equivalence classes of an equivalence relation form a partition of the set. Consider the set ℕ with the equivalence relation ≡ defined by the rule: a≡b in ℕ...
Discrete Math Course 3. Decide and explain whether or not S is an equivalence relation on...
Discrete Math Course 3. Decide and explain whether or not S is an equivalence relation on Z , if ??? ??? 3 ??????? ?+2? 4. Find the transitive closure of the relation ?={(?,?),(?,?),(?,?),(?,?),(?,?)} on the set ?={?,?,?,?,?}. Draw a directed graph of ? (not its closure). 5. Decide and explain whether or not the set ?={?/4∶?∈?} is a countable
Let a1 = [ 7 2 -1 ] a2 =[ -1 2 3 ] a3= [...
Let a1 = [ 7 2 -1 ] a2 =[ -1 2 3 ] a3= [ 6 4 9 ] a.)determine whether a1 a2 and a3span R3 b.) is a3 in the Span {a1, a2}?
Let ​R​ be an equivalence relation defined on some set ​A​. Prove using mathematical induction that...
Let ​R​ be an equivalence relation defined on some set ​A​. Prove using mathematical induction that ​R​^n​ is also an equivalence relation.
2. Let R be a relation on the set of integers ℤ defined by ? =...
2. Let R be a relation on the set of integers ℤ defined by ? = {(?, ?): a2 + ?2 ?? ? ??????? ??????} Is this relation reflexive? Symmetric? transitive?
Let R be the relation on the set A = {1,2,3,4,5} where aRb exactly when |a−b|...
Let R be the relation on the set A = {1,2,3,4,5} where aRb exactly when |a−b| = 1. Let S be the relation on the set A where aSb exactly when a = 1 or b = 4. 1. Find matrix representations and digraph representations for both R and S. 2. Find matrix representations for ¯ R and S^−1. 3. Find digraph representations for R∩S and R◦S.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT