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)
13. Let R be a relation on Z × Z be defined as (a, b) R...
13. Let R be a relation on Z × Z be defined as (a, b) R (c, d)
if and only if a + d = b + c.
a. Prove that R is an equivalence relation on Z × Z.
b. Determine [(2, 3)].
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.