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Identifying a Function from a Set of Ordered Pairs
publish date: 2026/05/23 22:20:49.336882 UTC
volume_mute
Let \(A = \{1, 2, 3, 4\}\) and \(B = \{2, 4, 5\}\). Which of the following relations from \(A\) to \(B\) is a function?
Correct Answer
\(R_4 = \{(1, 4), (2, 5), (3, 2), (4, 4)\}\)
Explanation
\(R_4\) is a function because each element of \(A = \{1,2,3,4\}\) appears exactly once as a first component. Check the others: \(R_1\) fails because 1 appears twice and 3 appears twice. \(R_2\) fails because 2 and 3 never appear as first components. \(R_3\) fails because 2 never appears as a first component, and 3 appears three times.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012