Which of the following relations from \(A=\{1,2,3,4\}\) to \(B=\{1,2,3,4\}\) is the identity function?

Correct answer: \(R=\{(1,1),(2,2),(3,3),(4,4)\}\)

In an identity function, every \(x\in A\) maps to itself, so \(I_A(x)=x\). In option A, the mappings are \(1\to1, 2\to2, 3\to3\), and \(4\to4\); hence it is the identity function. Option C is a constant function, while B and D map at least some elements to different elements. Exam tip: for an identity function, check whether every ordered pair has equal components, \((x,y)\) with \(x=y\).