volume_mute

Empty Relation as a Function

publish date: 2026/05/23 22:20:51.396003 UTC

Let \(A = \{1, 2\}\) and \(B = \{3, 4\}\). Is the empty relation \(R = \varnothing\) a function from \(A\) to \(B\)?

Yes, because the empty set is a subset of \(A \times B\)

No, because it violates the condition that every element of \(A\) must have an image

Yes, but only if \(A\) is also empty

No, because a function must contain at least one ordered pair

Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012