Types of relations

Correct answer: A. 7

Step 1: \((g\circ f)(2)=g(f(2))\). Compute the inner function: \(f(2)=2\cdot2-1=3\). Then evaluate the outer function: \(g(3)=3+4=7\). Thus the correct answer is 7. The closest distractor 6 results from mistakenly evaluating \(g(2)=6\) instead of \(g(f(2))\). Exam tip: for compositions, always evaluate the inner function first (find \(f(x)\)), then apply the outer function.

Correct answer: C. Identity relation

The condition a = b allows exactly those ordered pairs whose first and second components are the same. Thus R = {(a,a) : a ∈ A}, which is the identity relation on A, commonly denoted by I_A. It contains every diagonal pair and no off-diagonal pair. It is therefore reflexive, because every element is related to itself, and it is also symmetric and transitive; however, the question asks for its name, not merely one of its properties. The universal relation would contain every pair in A × A, whereas the empty relation contains none. An inverse relation is obtained by reversing pairs of a given relation and is not the definition used here. Hence option C is correct.