Discrete Math: A ∨ B = A ⋃ B?

Problem from "Discrete Mathematics with Graph Theory"

by Goodaire and Parmenter

Page 69 # 12b

Let S be a nonempty set and let A and B be elements of the power set of S. In the partially ordered (ℙ(S), ⊆)

Prove A ∨ B = A ⋃ B

1 Answer

  • 9 years ago
    Favorite Answer

    A∨B is the greatest lower bound of A ⋃ B in the partial ordering induced by ⊆.

    To be shown:

    A ⋃ B ⊆ A

    A ⋃ B ⊆ B

    therefore A ⋃ B ⊆ A V B.

    If C ⊆ A and C ⊆ B, then C ⊆ A U B

    therefore A V B ⊆ A U B.

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