Which option shows that the relation is not a function because 2 of A={1,2,3} is missing?

Correct answer: {(1,5),(3,7)}

The direct answer is A: {(1,5),(3,7)}. A function from A to another set must assign exactly one output to every element of its domain. Here the domain is A = {1,2,3}, so 1, 2, and 3 must all appear as first components. In option A, first components are only 1 and 3; 2 is missing. Thus this relation is not a function from A because the domain element 2 has no image. Option A is correct. Option B contains first components 1, 2, and 3, and each appears once, so it is a function. Option C also includes all three domain elements; two different inputs may have the same output, so it is still a function. Option D includes 1, 2, and 3 exactly once, so it is also a function. The common mistake is thinking that outputs must be different. They need not be different; only each input must have one and only one output. Memory cue: check the first coordinates, cover every domain element exactly once.