Decide, with justification, if the following set properties are true for any sets A, B, and...

Decide, with justification, if the following set properties are true for any sets A, B, and C.

1. A∪(B∩C)⊆A.

2. A∪(B∩C)⊆B.

3. A ∩ B ⊆ A

4. B ⊆ A ∪ B
5. A ⊆ B ⇒ A ∪ B ⊆ B.

6. A ∪ B ⊆ B ⇒ A ⊆ B.

7. A⊆B⇒A∩B=A.

8. A ∩ B = A ⇒ A ⊆ B
9. A∩(B∪C)⊆A∪(B∩C)
10. A∪(B∩C)⊆A∩(B∪C)
11. A\(B∩C)=(A\B)∪(A\C)

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Expert Solution

Colby Messinger answered 3 months ago

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