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 binary relation R on {a, b,
c} where R={(a, a), (b, b)), (c,...
Determine whether the binary relation R on {a, b,
c} where R={(a, a), (b, b)), (c, c), (a, b), (a,
c), (c, b) } is:
a.
reflexive, antisymmetric, symmetric
b.
transitive, symmetric, antisymmetric
c.
antisymmetric, reflexive, transitive
d.
symmetric, reflexive, transitive
Let A be the set of all lines in the plane. Let the relation R
be...
Let A be the set of all lines in the plane. Let the relation R
be defined as:
“l1 R l2 ⬄ l1 intersects
l2.” Determine whether S is reflexive, symmetric, or
transitive. If the answer is “yes,” give a justification (full
proof is not needed); if the answer is “no” you must give a
counterexample.
Construct a binary relation R on a nonempty set A satisfying the
given condition, justify your...
Construct a binary relation R on a nonempty set A satisfying the
given condition, justify your solution.
(a) R is an equivalence relation.
(b) R is transitive, but not symmetric.
(c) R is neither symmetric nor reflexive nor transitive.
(d) (5 points) R is antisymmetric and symmetric.
Determine whether the relation R is reflexive, symmetric,
antisymmetric, and/or transitive [4 Marks]
22
The relation...
Determine whether the relation R is reflexive, symmetric,
antisymmetric, and/or transitive [4 Marks]
22
The relation R on Z where (?, ?) ∈ ? if ? = ? .
The relation R on the set of all subsets of {1, 2, 3, 4} where
SRT means S C T.
Let R be the relation on the set of real numbers such that xRy
if and...
Let R be the relation on the set of real numbers such that xRy
if and only if x and y are real numbers that differ by less than 1,
that is, |x − y| < 1. Which of the following pair or pairs can
be used as a counterexample to show this relation is not an
equivalence relation?
A) (1, 1)
B) (1, 1.8), (1.8, 3)
C) (1, 1), (3, 3)
D) (1, 1), (1, 1.5)
Consider the relation R defined on the real line R, and defined
as follows: x ∼...
Consider the relation R defined on the real line R, and defined
as follows: x ∼ y if and only if the distance from the point x to
the point y is less than 3. Study if this relation is reflexive,
symmetric, and transitive. Which points are related to 2?