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}.
Consider the following relation on the set Z: xRy ?
x2 + y is even.
For...
Consider the following relation on the set Z: xRy ?
x2 + y is even.
For each question below, if your answer is "yes", then prove it, if
your answer is "no", then show a counterexample.
(i) Is R reflexive?
(ii) Is R symmetric?
(iii) Is R antisymmetric?
(iv) Is R transitive?
(v) Is R an equivalence relation? If it is, then describe the
equivalence classes of R. How many equivalence classes are
there?
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...
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...