Analysis of Universal Sets and Subset Properties

Analysis of Universal Sets and Subset Properties

Secondary 4

Given that the universal set is the set of positive even integers and that \(A = \{x : 30 < 3x < 62\}\) and \(B = \{x : x - 1 < 17 < x + 11\}\).

  1. List the elements of set \(A\) and set \(B\).
  2. Find \(n(A' \cap B)\).
  3. Describe, as simply as possible, in words, the elements contained in the set \(C\) where \(C = \{8, 12, 16\}\).

All sets in this question are subsets of the stated universal set \(\xi\); every set-builder variable is restricted to that universe.

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Answer:(a) \(A=\{12,14,16,18,20\}\), \(B=\{8,10,12,14,16\}\) (b) \(2\) (c) multiples of \(4\) from \(8\) to \(16\) inclusive

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