Let R be the relation on Z defined by:
For any a, b ∈ Z ,...
Let R be the relation on Z defined by:
For any a, b ∈ Z , aRb if and only if 4 | (a + 3b). (a) Prove that
R is an equivalence relation.
(b) Prove that for all integers a and b, aRb if and only if a ≡
b (mod 4)
Let
A be the set of all integers, and let R be the relation "m divides...
Let
A be the set of all integers, and let R be the relation "m divides
n." Determine whether or not the given relation R, on the set A, is
reflexive, symmetric, antisymmetric, or transitive.
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