Question

(1) (2 points) List all of the ordered pairs in the relation R = {(a, b)|a + b is even} on the set {1, 2, 3, 4, 5} (2) (4 points) Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric, and/or transitive, where (a, b) ∈ R if and only if (a) There is a book that both a and b have read. (b) a has a higher GPA than b. (3) (4 points) Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ∈ R if and only if (a) x − y = 0 (b) x < y ∨ y < x (4) (2 points) Which, if any, of the relations from problems 4.1, 4.2, and 4.3 are equivalence relations?

          (1) (2 points) List all of the ordered pairs in the relation R =
{(a, b)|a + b is even} on the set {1, 2, 3, 4, 5}
(2) (4 points) Determine whether the relation R on the set of
all people is reflexive, symmetric, antisymmetric, and/or
transitive, where (a, b) ∈ R if and only if (a) There is a book
that both a and b have read.
(b) a has a higher GPA than b.
(3) (4 points) Determine whether the relation R on the set of
all real numbers is reflexive, symmetric, antisymmetric, and/or
transitive, where (x, y) ∈ R if and only if (a) x − y = 0 (b) x
< y ∨ y < x
(4) (2 points) Which, if any, of the relations from problems
4.1, 4.2, and 4.3 are equivalence relations?

Added by Dawn G.

Question

Please give Ace some feedback