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
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 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,...
For each of the following relations on the set {1, 2, 3, 4}
(a) { (1,...
For each of the following relations on the set {1, 2, 3, 4}
(a) { (1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (2,
3), (2, 4), (3, 3), (3, 4), (4, 4) }
(b) { (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)
}
(c) { (2, 4}, (4, 2) }
(d) ( (1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)
}
Choose all answers that apply.
Group of...
Let A = {1,2,3,4,5} and X = P(A) be its powerset. Define a
binary relation on...
Let A = {1,2,3,4,5} and X = P(A) be its powerset. Define a
binary relation on X by for any sets S, T ∈ X, S∼T if and only if S
⊆ T.
(a) Is this relation reflexive?
(b) Is this relation symmetric or antisymmetric?
(c) Is this relation transitive?
Complete the following table. If a property does not hold give
an example to show why...
Complete the following table. If a property does not hold give
an example to show why it does not hold.
If it does hold, prove or explain why. Use correct symbolism.
(Just Yes or No is incorrect)
R = {(a,b) | a,b ∃ Z: : a + b-even
S = {(a,b) | a,b ∃ Z: : a + b-odd
T = {(a,b) | a,b ∃ Z: : a + 2b-even
Relation
Reflexive
Symmetric
Anti Symmetric
Neither Symmetric or anti-symmetric
Transitive...