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.
Let A = {−5, −4, −3, −2, −1, 0, 1, 2, 3} and define a relation...
Let A = {−5, −4, −3, −2, −1, 0, 1, 2, 3} and define a relation R
on A as follows: For all (m, n) is in A, m R n ⇔ 5|(m2 − n2). It is
a fact that R is an equivalence relation on A. Use set-roster
notation to list the distinct equivalence classes of R. (Enter your
answer as a comma-separated list of sets.)
____________
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?
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...
Let R be the relation on the set of real numbers such that xRy
if and...
Let R be the relation on the set of real numbers such that xRy
if and only if x and y are real numbers that differ by less than 1,
that is, |x − y| < 1. Which of the following pair or pairs can
be used as a counterexample to show this relation is not an
equivalence relation?
A) (1, 1)
B) (1, 1.8), (1.8, 3)
C) (1, 1), (3, 3)
D) (1, 1), (1, 1.5)