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Prove that if A1 ,A2 ,…,An and B are sets, then _______.

a) A1 ∪ A2 ∪…∪ An =B
b) A1 ∩ A2 ∩…∩ An =B
c) A1 ∩ A2 ∩…∩ A n ⊆B
d) A1 ∪ A2 ∪…∪ An ⊆B

User Chelsea
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Final answer:

Option B. Without specific information about the relationship between given sets, we cannot prove which, if any, of the statements concerning their union or intersection equals or is a subset of another set B.

Step-by-step explanation:

The question seems to be asking to prove that the union or intersection of sets A1, A2, …, An relates to set B in a particular way. However, without any specific information about the relationship between sets A1, A2, ..., An, and B, we cannot prove any of the following statements to be correct:

  • A1 ∪ A2 ∪…∪ An = B
  • A1 ∩ A2 ∩…∩ An = B
  • A1 ∩ A2 ∩…∩ An ⊆ B
  • A1 ∪ A2 ∪…∪ An ⊆ B

Each statement above assumes a very specific condition between these sets, such as exactly equal set union or intersection, or subset relationships. It's also worth noting that the notations used denote the following: '∪' is set union, '∩' is set intersection, and '⊆' denotes subset. To evaluate these statements, one would typically need to know the exact elements contained in each of the sets or a defined property that relates them. Given the lack of information, we cannot substantiate these claims.

User Viktortnk
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