Let ∼ ⊆ X ∗X be an equivalence relation on a set X. For x ∈ X define ̄x := {y ∈ X |x ∼ y}. Then it holds that P := { ̄x
Posted: Sun May 15, 2022 11:37 am
Let ∼ ⊆ X ∗X be an equivalence relation on a set X. For x ∈
X
define ̄x := {y ∈ X |x ∼ y}. Then it holds that P := { ̄x |x ∈ X}
is a
partition of X.
i) Give the definition of a partition.
ii) Prove that P is a partition.
X
define ̄x := {y ∈ X |x ∼ y}. Then it holds that P := { ̄x |x ∈ X}
is a
partition of X.
i) Give the definition of a partition.
ii) Prove that P is a partition.