Question

In: Advanced Math

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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