1) Define the relation R on the set of integer numbers (ℤ) by xRy if xy > 0. Is R an equivalence relation? Justify. 2) Let R, the relation R on ℤ by aRb if a2 - b2  3. Is R an equivalence relation? Justify.
3) Let r be the relation on the set of integer numbers (ℤ) such that arb if and only if a + b is odd. Is r an equivalence relation?
4) Let R be a relation defined on the set ℤ by aRb if a  b. Is it true that R is symmetric and transitive? If not, give an example.
5) Let A = {1, 2, 3, 4, 5}, and let
R = {(3,4), (5,5), (1,1), (2,2), (5,2), (1,4), (2,5), (3,1), (3,3), (4,1), (1,3), (4,3), (4,4)} be an equivalence relation on A. Find the [1] and [3] on R.
1) Consider the function f: R → R defined by f(x) = 2x +3. R - set of real numbers
A) Find the inverse function of the function f.
B) Is f o f-1= f-1 o f
2) Prove that the function f: R {2} → R (5) defined by f(x) = is bijective R defined by f(x) = x + 1 is a surjection (onto).
3. Determine if the function f: R t of real numbers.