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.
Let
A = {1,2,3,4,5,6,7,8,9,10} define the equivalence relation R on A
as follows : For all...
Let
A = {1,2,3,4,5,6,7,8,9,10} define the equivalence relation R on A
as follows : For all x,y A, xRy <=> 3|(x-y) . Find the
distinct equivalence classes of R(discrete math)
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...