大师作文网证明1.Let A,B,and C be sets.Prove thatA∪包含 (A∪B ∪C).2.Let A,B,
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证明
1.Let A,B,and C be sets.Prove that
A∪包含 (A∪B ∪C).
2.Let A,B,and C be sets.Prove that
(A-C)∩(C -B) = 空集
1.Let A,B,and C be sets.Prove that
A∪包含 (A∪B ∪C).
2.Let A,B,and C be sets.Prove that
(A-C)∩(C -B) = 空集
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 of
one of A,B,C.that means a a∈A∪B ∪C
case 2:a∈B,similarly discuss.
so in both cases,a must be member of A∪B ∪C
that means A∪B is subset of ∪B ∪C
2.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.
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 of
one of A,B,C.that means a a∈A∪B ∪C
case 2:a∈B,similarly discuss.
so in both cases,a must be member of A∪B ∪C
that means A∪B is subset of ∪B ∪C
2.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.
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