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Question

Difficulty: EasySets and Set Operations

Let the universal set be U={1,2,3,4,5,6,7,8,9,10}\mathcal{U} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} and set P={2,3,5,7}P = \{2, 3, 5, 7\}. Which of the following is the complement of set PP, denoted by P′P'?

  1. {1,4,6,8,9,10}\{1, 4, 6, 8, 9, 10\}Answer
  2. B
    {1,3,5,7,9}\{1, 3, 5, 7, 9\}
  3. C
    {4,6,8,10}\{4, 6, 8, 10\}
  4. D
    {2,3,5,7}\{2, 3, 5, 7\}

Answer

{1,4,6,8,9,10}\{1, 4, 6, 8, 9, 10\}
The complement of set PP, denoted as P′P', consists of every element in the universal set U\mathcal{U} that is not present in set PP. Removing 2,3,5,72, 3, 5, 7 from {1,2,3,4,5,6,7,8,9,10}\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} leaves {1,4,6,8,9,10}\{1, 4, 6, 8, 9, 10\}.

Step-by-Step Solution

1
Identify elements of the universal set U\mathcal{U} and set PP
U={1,2,3,4,5,6,7,8,9,10}\mathcal{U} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} and P={2,3,5,7}P = \{2, 3, 5, 7\}
The complement set requires comparing set PP against the universal set.
2
Remove elements of set PP from U\mathcal{U} to find P′P'
P′=U∖P={1,4,6,8,9,10}P' = \mathcal{U} \setminus P = \{1, 4, 6, 8, 9, 10\}
By definition, the complement P′P' consists of all elements in U\mathcal{U} that do not belong to PP.

Key Concept

Set Complement
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Topics

Sets and Set Operations

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