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.
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}.
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,...
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
Show that reflexive sentences are independent from symmetric,
and transitive sentences by constructing a structure that...
Show that reflexive sentences are independent from symmetric,
and transitive sentences by constructing a structure that satisfy
symmetric and transitive quality but not reflexive.
Reflexive :∀xE(x, x)
symmetric :∀xy(E(x, y) → E(y, x))
transitive: ∀xyz(E(x, y) ∧ E(y, z) → E(x, z))
Show that symmetric sentences are independent from reflexive,
and transitive sentences by constructing a structure that...
Show that symmetric sentences are independent from reflexive,
and transitive sentences by constructing a structure that satisfy
transitive and reflexive quality but not symmetric.
Reflexive :∀xE(x, x)
symmetric :∀xy(E(x, y) → E(y, x))
transitive: ∀xyz(E(x, y) ∧ E(y, z) → E(x, z))
Give examples of the following relationships:
a) A transitive and symmetrical relationship, but not
reflexive.
b)...
Give examples of the following relationships:
a) A transitive and symmetrical relationship, but not
reflexive.
b) A symmetric and reflexive relationship, but not
transitive.
c) An antisymmetric and thoughtless relationship.
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 relation R on N is reflexive, symmetric,
and/or transitive. Prove your answer.
a)R...
Determine whether the relation R on N is reflexive, symmetric,
and/or transitive. Prove your answer.
a)R = {(x,y) : x,y ∈N,2|x,2|y}.
b)R = {(x,y) : x,y ∈ A}. A = {1,2,3,4}
c)R = {(x,y) : x,y ∈N,x is even ,y is odd }.
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.