If R is symmetric, which statement about R⁻¹ is correct?

Correct answer: R⁻¹ = R

For any relation R, the inverse R⁻¹ is formed by interchanging the coordinates of every ordered pair: (a,b) in R produces (b,a) in R⁻¹. If R is symmetric, that reversed pair already belongs to R. Consequently, every element of R⁻¹ is an element of R, and the same reasoning applied to R⁻¹ shows that every element of R is an element of R⁻¹. The two relations are therefore equal: R⁻¹ = R. Symmetry does not imply that a relation is empty or universal; it only imposes a reverse-pair condition. Also, an inverse of a relation is always a relation on the corresponding reversed sets, so option C is impossible.