Union and intersection subsets mh - Rhea

Theorem

Let $ A $ and $ B $ be sets. Then
(a) (A ∩ B) ⊂ A
(b) A ⊂ (A ∪ B)

Proof

(a) let x ∈ (A ∩ B) ⇔ x ∈ A and x ∈ B ⇒ x ∈ A ⇒ (A ∩ B) ⊂ A.
(b) let x ∈ A. Then it is true that x is either in A or in B ⇔ x ∈ (A ∪ B) ⇒ A ⊂ (A ∪ B).
$ \blacksquare $

References

• B. Ikenaga, "Set Algebra and Proofs Involving Sets" March 1st, 2008, [October 1st, 2013]

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