## Trending News

Promoted

# 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

Relevance

- vekkus4Lv 69 years agoFavorite 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.

Still have questions? Get your answers by asking now.