Prove that if A, B, and C are arbitrary sets and A −C ⊈ A −B, then B ⊈ C. I dont know how to prove this. I want to  contrapostive B⊆C, then A-C ⊆ A-B.

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Q: Show that A ∪ B = A ∩ B implies A = B

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Q: Prove that (ab + cd)² ≤ (a² + c²)(b² + ď²) for all a, b, c, d ɛ R.

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A: To Prove- Prove that if A1, A2, ...., An and B are sets, then A1 - B ∪ A2 - B ∪ .... ∪ An - B = A1 ∪…

Q: 1. Determine which of the following statements are true for all sets A, B, C, and D. If a double…

A: .

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Q: Prove or disprove: For all sets A, B, we must have 24A2(AAB) = 2B.

A: Given, 2A∆2A∆B

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Q: A = {−1,0,1,2,3}, B = {12,1,4}, C = {x|0 < x ≤ 2}, D = (−1,1]. Find each of the following sets: 6.…

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A: No, this is not true in general. For example, consider the following :

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A: We construct  an example of three sets A,B and C such that A ⊆ B, B ⊆ C, C 6⊆ A and C ⊆ B.

Q: Prove that A-B = A iff A intersection B = null set

A: From the given information it is required to prove that:

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A: A∪B-C=A-C∪B-C

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A: Since you have posted a question with multiple sub ports, we will provide the solution only to the…

Q: Let A and B be sets. The symmetric difference of A and B, denoted A∆B, is the set A∆B = (A −B) ∪(B…

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Q: If n(A ∪ B) = 2n(A), then A and B are equivalent sets.

A: Here use definition of equivalent set