If (f:A\to B) where (A={2,4}) and (B={1,3,5}), which form of (f) can be a function?

Correct answer: ({(2,1),(4,5)})

Direct answer: Option A, \(\{(2,1),(4,5)\}\). For a function from \(A=\{2,4\}\) to \(B=\{1,3,5\}\), every element of A must occur exactly once as a first component, and each second component must belong to B. In option A, 2 is mapped to 1 and 4 is mapped to 5; both outputs are in B, and each input has exactly one image. Option B is invalid because input 2 is assigned both 1 and 3, while input 4 has no image. Option C is invalid because input 2 has no image. Option D is invalid because input 4 is assigned two different outputs, 5 and 3, while input 2 has one. The fact that 3 is unused in option A does not matter; a function need not use every codomain element. Memory cue: check the first coordinates—each domain element must appear once and only once.