If (A={1,2,3}) and (B={4,5}), which statement is correct about (R={(1,4),(2,5),(3,4)})?

Correct answer: It is a function from (A) to (B)

The direct answer is A: \(R\) is a function from \(A\) to \(B\). For a function from \(A\) to \(B\), every element of the domain \(A\) must have exactly one image in \(B\). Check the first entries: 1 is paired with 4, 2 with 5, and 3 with 4. Thus every member of \(A\) appears once as an input, and every second entry is in \(B=\{4,5\}\). Repetition of an output is allowed; different inputs may have the same image. Therefore A is correct. Option B is wrong because 4 appearing twice is not a problem: both 1 and 3 may map to 4. Option C is wrong because 5 need not appear more than once; a codomain element may be unused or used once or several times. Option D is wrong because the stated mapping is from A to B, not only from B to A, and B has no obligation to supply the inputs. Exam cue: inspect first components and demand exactly one pair for each domain element.