Which relation from (A={1,2,3}) to (B={p,q,r}) is not a function?

Correct answer: (R={(1,p),(2,q),(2,r),(3,p)})

The direct answer is C. A function must assign every element of the domain exactly one image in the codomain. In option C, the input 1 is paired with p, input 3 with p, but input 2 is paired with both q and r. Since q and r are different outputs, one input has two images, so this relation is not a function. Option A is a function: 1, 2, and 3 each have exactly one image, namely p, q, and r. Option B is also a function: different inputs are allowed to have the same output p; a function does not require different outputs. Option C fails the one-output rule because of (2,q) and (2,r). Option D is a function because each domain element has one image, even though the order of the outputs is reversed. The useful test is to inspect the first coordinates: every domain element must occur once with only one second coordinate.