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Determining if a Relation is a Function
publish date: 2026/05/23 22:20:50.801829 UTC
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Let \(A = \{1, 2, 3, 4\}\). Which of the following relations on \(A\) (i.e., from \(A\) to \(A\)) is a function?
Correct Answer
\(\{(1, 2), (2, 3), (3, 4), (4, 1)\}\)
Explanation
Check each: Option 1 has each of 1,2,3,4 exactly once as first components → function. Option 2 has 1 appearing twice as first component → not a function. Option 3 has 2 appearing twice as first component → not a function. Option 4 is missing 4 as a first component (not total) → not a function from A to A.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012