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

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answerhappygod
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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

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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.
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