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Relations & Functions · Question 108 of 125

Question 108

MediumOriginal question

f:A→Bf : A \to B is onto and AA has 5 elements. What is the largest number of elements BB can have?

Options for question 108

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. Every element of BB must be the image of at least one element of AA.

  2. 5 elements give at most 5 different images.

Worth noting

32 is 252^{5}, the number of subsets of AA; it has nothing to do with the images.

Concept
Sizes of the sets in an onto function
Typical time
90 s
Your time
—
The rule this testsOnto and bijective functions
Practise this chapter →

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

Practise this chapter →

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