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Properties of Finite Sets and Venn Diagrams

Properties of Finite Sets and Venn Diagrams

TGM Original

It is given that \(\xi = \{x : x \text{ is a whole number and}\hspace{0.5em} 0 < x < 13\}\), \(P = \{x : x \text{ is a multiple of}\hspace{0.5em} 6\}\) and \(Q = \{x : x \text{ is an even number}\hspace{0.15em}\}\).

  1. List the elements of \(Q\).
  2. Draw a clearly labelled Venn diagram to illustrate the information.
  3. Copy the Venn diagram in (b) and shade the region that represents \(P \cup Q'\).
  4. Find the number of elements in \(P \cup Q'\).

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

Solution:

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Answer:(a) \(Q=\{2,4,6,8,10,12\}\) (b) \(P=\{6,12\}\) inside \(Q\), \(Q\) only \(=\{2,4,8,10\}\), outside \(Q=\{1,3,5,7,9,11\}\) (c) Shade \(P\) and \(Q'\). (d) \(8\)

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