Determine whether the following is reflexive, symmetric,
antisymmetric, transitive, and/or a partial order:
(x, y) ∈...
Determine whether the following is reflexive, symmetric,
antisymmetric, transitive, and/or a partial order:
(x, y) ∈ R if 3 divides x – y
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
For each of the properties reflexive, symmetric, antisymmetric,
and transitive, carry out the following.
Assume that...
For each of the properties reflexive, symmetric, antisymmetric,
and transitive, carry out the following.
Assume that R and S are nonempty relations on a set A that both
have the property. For each of Rc, R∪S, R∩S, and R−1, determine
whether the new relation
must also have that property;
might have that property, but might not; or
cannot have that property.
A ny time you answer Statement i or Statement iii, outline a
proof. Any time you answer Statement ii,...
Disprove: The following relation R on set Q is either reflexive,
symmetric, or transitive. Let t...
Disprove: The following relation R on set Q is either reflexive,
symmetric, or transitive. Let t and z be elements of Q. then t R z
if and only if t = (z+1) * n for some integer n.
For each of the following relations, determine whether the
relation is reflexive, irreflexive, symmetric, antisymmetric, and/or...
For each of the following relations, determine whether the
relation is reflexive, irreflexive, symmetric, antisymmetric, and/or
transitive. Then find R−1.
a) R = {(x,y) : x,y ∈Z,x−y = 1}.
b) R = {(x,y) : x,y ∈N,x|y}.
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.
Let
A be the set of all real numbers, and let R be the relation "less...
Let
A be the set of all real numbers, and let R be the relation "less
than." Determine whether or not the given relation R, on the set A,
is reflexive, symmetric, antisymmetric, or transitive.
Consider the relation R= {(1,2),(2,2),(2,3),(3,1),(3,3)}. Is R
transitive, not reflexive, symmetric or equivalence relation?
Consider the relation R= {(1,2),(2,2),(2,3),(3,1),(3,3)}. Is R
transitive, not reflexive, symmetric or equivalence relation?
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.