证明1.Let A,B,and C be sets.Prove thatA∪包含 (A∪B ∪C).

证明1.Let A,B,and C be sets.Prove thatA∪包含 (A∪B ∪C).

1、Pick a∈A∪B ,then a a∈A or a∈B.there are two cases:case 1 :a∈A,then a must be a member ofone of A,B,C.that means a a∈A∪B ∪Ccase 2:a∈B,similarly discuss.so in both cases,a must be member of A∪B ∪Cthat means A∪B is subset of ∪B ∪C2.Pick a∈(A-C),a must be in A and not in C.because a is not C,a is not in C-B.so,for every element a ,a can not be in both (A-C) and (B-C).that means (A-C)∩(C -B) has no element.therefore,(A-C)∩(C -B) is empty set.======以下答案可供参考======供参考答案1:1，如果证明A∪B包含 (A∪B ∪C)任取x属于A∪B它要么在A中,要么在B中所以也一定在 (A∪B ∪C)中所以成立2，因为(A-C)里的元素是不属于C的，而(C -B) 中的元素都是属于C的所以它们不相交，所以是空集

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