Question

Prove that every equivalence relation induces a partition. Write the formal proof with usual notations.

Prove that every equivalence relation induces a partition. Write the formal proof with usual notations.

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

Homework Answers

Answer #1

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
Write a formal proof to prove the following conjecture to be true or false. If the...
Write a formal proof to prove the following conjecture to be true or false. If the statement is true, write a formal proof of it. If the statement is false, provide a counterexample and a slightly modified statement that is true and write a formal proof of your new statement. Conjecture: There does not exist a pair of integers m and n such that m^2 - 4n = 2.
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.
Prove that the relation of set equivalence is an equivalence relation.
Prove that the relation of set equivalence is an equivalence relation.
Write a formal proof where you define a function to prove that the sets 3Z and...
Write a formal proof where you define a function to prove that the sets 3Z and 6Z have the same cardinality, meaning |3 Z| = |6 Z|. 3Z = {..., −3, 0, 3, 6, 9, ...} and 6Z = {..., −6, 0, 6, 12, 18, ...} Z = integers
Prove: Proposition 11.13. Congruence modulo n is an equivalence relation on Z : (1) For every...
Prove: Proposition 11.13. Congruence modulo n is an equivalence relation on Z : (1) For every a ∈ Z, a = a mod n. (2) If a = b mod n then b = a mod n. (3) If a = b mod n and b = c mod n, then a = c mod n
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...
Prove that the Petersen graph P(5, 2) is the complement of L(K5) with a formal proof.
Prove that the Petersen graph P(5, 2) is the complement of L(K5) with a formal proof.
Prove that if T is a discrete topological space (i.e., every subset of T is open)...
Prove that if T is a discrete topological space (i.e., every subset of T is open) and ∼ is any equivalence relation on T , then the quotient space T / ∼ is also discrete topological space. [Hint: It is a very short and straightforward proof.]
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|
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT