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Relations & Functions · Question 27 of 125

Question 27

MediumOriginal question

How many relations on {1,2,3}\{1, 2, 3\} contain the pair (1,2)(1, 2)?

Options for question 27

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. (1,2)(1, 2) is fixed in; each of the other 9−1=89 - 1 = 8 pairs is in or out.

  2. 28=2562^{8} = 256.

Worth noting

29−12^{9} - 1 removes only the empty relation; half of all relations lack (1,2)(1, 2).

Concept
Counting relations
Typical time
90 s
Your time
—
The rule this testsTypes of relations
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Ten questions from Relations & Functions, at your own pace.

Practise this chapter →

Ten questions from Relations & Functions, at your own pace.