How a complement changes

How a complement changes

Secondary 3
3 marks
TGM Original Questions

A library initially considers books numbered 1 to 8, so \(\xi=\{1,2,\ldots,8\}\). The borrowed books form \(A=\{2,5,8\}\). Later, books 9 and 10 are added to the collection and neither is borrowed.

  1. List \(A'\) before the two books are added.[1]
  2. List \(A'\) in the enlarged universal set.[1]
  3. Explain why \(n(A)\) is unchanged but \(n(A')\) increases.[1]

Solution:

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Answer:(a) \(\{1,3,4,6,7\}\) (b) \(\{1,3,4,6,7,9,10\}\) (c) The new elements are in the complement only.

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