GATE DA 2025 — Question 30

Let \(C_1\) and \(C_2\) be two sets of objects. Let \(D(x, y)\) be a measure of dissimilarity between two objects \(x\) and \(y\). Consider the following definitions of dissimilarity between \(C_1\) and \(C_2\):

\(\text{DIS-1}(C_1, C_2) = \max_{x \in C_1, \, y \in C_2} D(x, y)\)

\(\text{DIS-2}(C_1, C_2) = \min_{x \in C_1, \, y \in C_2} D(x, y)\)

Which of the following statements is/are correct?