Question
In: Advanced Math
S = Z (integers), R = {(a,b) : a = b mod 5}. Is this relation...
S = Z (integers), R = {(a,b) : a = b mod 5}. Is this relation an equivalence relation on S?
S = Z (integers), R = {(a,b) : a = b mod 3}. Is this relation an equivalence relation on S? If so, what are the equivalence classes?
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Colby Messinger answered 2 years agoRelated Solutions
Show that the relation 'a R b if and only if a−b is an even integer defined on the Z of integers is an equivalence relation.
Show that the relation 'a R b if and only if a−b is an even integer defined on the Z of integers is an equivalence relation.
Let R be the relation on Z+× Z+ such that (a, b) R (c, d) if...
Let R be the relation on Z+× Z+ such that (a, b) R (c, d) if and
only if ad=bc. (a) Show that R is an equivalence relation. (b) What
is the equivalence class of (1,2)? List out at least five elements
of the equivalence class. (c) Give an interpretation of the
equivalence classes for R. [Here, an interpretation is a
description of the equivalence classes that is more meaningful than
a mere repetition of the definition of R. Hint:...
The equivalence relation on Z given by (?, ?) ∈ ? iff ? ≡ ? mod...
The equivalence relation on Z given by (?, ?) ∈ ? iff ? ≡ ? mod
? is an
equivalence relation for an integer ? ≥ 2.
a) What are the equivalence classes for R given a fixed integer ? ≥
2?
b) We denote the set of equivalence classes you found in (a) by
Z_5. Even though elements of Z_5 are
sets, it turns out that we can define addition and multiplication
in the expected ways: [?] + [?]...
Show that if a and b are integers with a ≡ b (mod p) for every...
Show that if a and b are integers with a ≡ b (mod p) for every
prime p, then it must be that a = b
Let S = {2 k : k ∈ Z}. Let R be a relation defined on...
Let S = {2 k : k ∈ Z}. Let R be a relation defined on Q− {0} by
x R y if x y ∈ S. Prove that R is an equivalence relation.
Determine the equivalence class
Give an example of integers a, b, m such that a 2 ≡ b 2 (mod...
Give an example of integers a, b, m such that a 2 ≡ b 2 (mod m),
but a 6≡ b (mod m)
On the set S of all real numbers, define a relation R = {(a, b):a ≤ b}. Show that R is transitive.
On the set S of all real numbers, define a relation R = {(a, b):a ≤ b}. Show that R is transitive.
Suppose A = {(a, b)| a, b ∈ Z} = Z × Z. Let R be...
Suppose A = {(a, b)| a, b ∈ Z} = Z × Z. Let R be the relation
define on A where (a, b)R(c, d) means that 2 a + d = b + 2 c.
a. Prove that R is an equivalence relation.
b. Find the equivalence classes [(−1, 1)] and [(−4, −2)].
Find all x ∈ Z such that x≡2 mod 221 and x≡5 mod 184.
Find all x ∈ Z such that x≡2 mod 221 and x≡5 mod 184.
6. Let R be a relation on Z x Z such that for all ordered pairs...
6. Let R be a relation on Z x Z such that for all ordered pairs
(a, b),(c, d) ∈ Z x Z, (a, b) R (c, d) ⇔ a ≤ c and b|d . Prove that
R is a partial order relation.
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