Question

Let us say that two integers are near to one another provided their difference is 2 or smaller (i.e., the numbers are at most 2 apart). For example, 3 is near to 5, 10 is near to 9, but 4 is not near to 8. Let R stand for this is-near-to relation. (a) Write down R as a set of ordered pairs. Your answer should look like this: R = {(x, y) : . . .}. (b) Prove or disprove: R is reflexive. (c) Prove or disprove: R is irreflexive. (d) Prove or disprove: R is symmetric. (e) Prove or disprove: R is antisymmetric. (f) Prove or disprove: R is transitive.

Answer #1

Hope this answer was helpful to you. If you satisfied with this answer give a thumps up.

Happy Learning :)

Let F = {A ⊆ Z : |A| < ∞} be the set of all finite sets of
integers. Let R be the relation on F defined by A R B if and only
if |A| = |B|. (a) Prove or disprove: R is reflexive. (b) Prove or
disprove: R is irreflexive. (c) Prove or disprove: R is symmetric.
(d) Prove or disprove: R is antisymmetric. (e) Prove or disprove: R
is transitive. (f) Is R an equivalence relation? Is...

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.

It had been a busy day for Marsha Chamberland. She had spent
most of it cleaning and running errands in prepara- tion for her
brother-in-law Ed’s return, and now she was preparing a quick
dinner for her family. Ed, an industry official whose job it was to
decide whether or not new products needed premarket approval by the
U.S. Food and Drug Administration, had spent the last two weeks in
Tennessee expressing his views on genetic engineering in food. He...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 14 minutes ago

asked 15 minutes ago

asked 35 minutes ago

asked 42 minutes ago

asked 50 minutes ago

asked 56 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago