Question

Give an example of a relation on the reals that is reflexive and symmetric, but not transitive

Answer #1

Consider a relation on the set of real numbers such that :

Now,

- If we consider,
for
then,
.
**Therefore, the relation is reflexive.**

Next,

- If ,

**Therefore the relation
is symmetric.**

But

- But, if we take

**Therefore, the relation
is not transitive.**

show that the relation "≈" is reflexive, symmetric, and
transitive on the class of all sets.

The subgroup relation ≤ on the set of subgroups G is reflexive,
transitive, and anti-symmetric.

Consider the relation R= {(1,2),(2,2),(2,3),(3,1),(3,3)}. Is R
transitive, not reflexive, symmetric or equivalence 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.

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.

1)
(a) Provide an example of a symmetric relation
on the set S={1,2,3,4,5}S={1,2,3,4,5} that is not transitive.
(b) Provide an example of a transitive
relation on the set S={1,2,3,4,5}S={1,2,3,4,5} that is not
symmetric.

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.

Prove that strong connectivity is reflexive, transitive and
symmetric.

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 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))

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