Question

Consider the definition of equivalence class. Let A be the set {0,1,2,3,4}. Is it possible to...

Consider the definition of equivalence class. Let A be the set {0,1,2,3,4}. Is it possible to have an equivalence relation on A with the equivalence classes: {0,1,2} and {2,3,4}? Explain. (Hint: Think about the element 2)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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...
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.
Let S be a finite set and let P(S) denote the set of all subsets of...
Let S be a finite set and let P(S) denote the set of all subsets of S. Define a relation on P(S) by declaring that two subsets A and B are related if A and B have the same number of elements. (a) Prove that this is an equivalence relation. b) Determine the equivalence classes. c) Determine the number of elements in each equivalence class.
Suppose R is an equivalence relation on a finite set A, and every equivalence class has...
Suppose R is an equivalence relation on a finite set A, and every equivalence class has the same cardinality m. Express |R| in terms of m and |A|. Explain why the answer is m|A|
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.
Consider the following relation ∼ on the set of integers a ∼ b ⇐⇒ b 2...
Consider the following relation ∼ on the set of integers a ∼ b ⇐⇒ b 2 − a 2 is divisible by 3 Prove that this is an equivalence relation. List all equivalence classes.
Recall from class that we defined the set of integers by defining the equivalence relation ∼...
Recall from class that we defined the set of integers by defining the equivalence relation ∼ on N × N by (a, b) ∼ (c, d) =⇒ a + d = c + b, and then took the integers to be equivalence classes for this relation, i.e. Z = [(a, b)]∼ | (a, b) ∈ N × N . We then proceeded to define 0Z = [(0, 0)]∼, 1Z = [(1, 0)]∼, − [(a, b)]∼ = [(b, a)]∼, [(a, b)]∼...
Let N* be the set of positive integers. The relation ∼ on N* is defined as...
Let N* be the set of positive integers. The relation ∼ on N* is defined as follows: m ∼ n ⇐⇒ ∃k ∈ N* mn = k2 (a) Prove that ∼ is an equivalence relation. (b) Find the equivalence classes of 2, 4, and 6.
a) Let R be an equivalence relation defined on some set A. Prove using induction that...
a) Let R be an equivalence relation defined on some set A. Prove using induction that R^n is also an equivalence relation. Note: In order to prove transitivity, you may use the fact that R is transitive if and only if R^n⊆R for ever positive integer ​n b) Prove or disprove that a partial order cannot have a cycle.
Problem 14. Consider the relation T on the set of all undergraduate/ graduate TAs ((U)TA) for...
Problem 14. Consider the relation T on the set of all undergraduate/ graduate TAs ((U)TA) for the CHE department where s1 T s2 if and only if s1 and s2 are (U)HAs for the same course. 14(a) Assuming that no one is a (U)TA for multiple courses, prove that T is an equivalence relation. 14(b) Assuming that no one is a (U)TA for multiple courses, what do the equivalence classes for T represent? 14(c) Assuming that no one is a...