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.
4. Let A={(1,3),(2,4),(-4,-8),(3,9),(1,5),(3,6)}. The relation R
is defined on A as follows: For all (a, b),(c,...
4. Let A={(1,3),(2,4),(-4,-8),(3,9),(1,5),(3,6)}. The relation R
is defined on A as follows: For all (a, b),(c, d) ∈ A, (a, b) R (c,
d) ⇔ ad = bc . R is an equivalence relation. Find the distinct
equivalence classes of 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. We define a relation C on the set of humans as xRy ⇐⇒ x and...
1. We define a relation C on the set of humans as xRy ⇐⇒ x and y
were born in the same country
Describe the equivalence class containing yourself as an
element.
2. Let R be an equivalence relation with (x, y) ∈ R and (y, z)
is not ∈ R (that is, y does not relate to z). Can you determine
whether or not xRz? Why or why not?
Let G be a graph with vertex set V. Define a
relation R from V to...
Let G be a graph with vertex set V. Define a
relation R from V to itself as follows: vertex
u has this relation R with vertex v,
u R v, if there is a path in G from u to
v. Prove that this relation is an equivalence relation.
Write your proof with complete sentences line by line in a logical
order. If you can, you may write your answer to this
question directly in the space provided.Your presentation
counts.
Determine whether the given relation is an equivalence relation
on {1,2,3,4,5}. If the relation is an...
Determine whether the given relation is an equivalence relation
on {1,2,3,4,5}. If the relation is an equivalence relation, list
the equivalence classes (x, y E {1, 2, 3, 4, 5}.)
{(1,1), (2,2), (3,3), (4,4), (5,5), (1,3), (3,1), (3,4),
(4,3)}
If the relation above is not an equivalence relation, state that
the relation is not an equivalence relation and why.
Example: "Not an equivalence relation. Relation is not
symmetric"
Remember to test all pairs in relation R