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...
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
In the following two problems, the equivalence classes refer to
the equivalence classes under the equivalence...
In the following two problems, the equivalence classes refer to
the equivalence classes under the equivalence relation:
aRb iff n|(a-b) where n is a fixed integer. Suppose a, b, c, d
are elements of the integers such that [a] = [b] and [c] = [d].
1. Prove [a+d] = [b+c].
2. Prove [ac] = [bd]