All subsets: {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}, {a, b, c} * * 8.

True set: empty set, {a}, {b}, {c}, {a, b}, {a, c}, {b, c} * * 7.

Non-empty space sets: {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c} * * 7.

2. Proof: = => (sufficiency): If A is contained in B, then any x∈A has x∈B,

Therefore, x∈(A∩B)

So a is included in (A ∩ B)-①.

For any x∈(A∩B), there obviously exists x∈A,

So (A∩B) is included in a-②.

From ① and ②: a ∩ b = a.

& lt= = (inevitable): if A∩B=A, then for any x∈A, that is, x∈A∩B, so x ∈ b.

That is, a is contained in B.

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I hope I can help you ~