Having now introduced some of the major classes studied in complexity theory, we next turn to the question of their internal structure. This can be studied using the notions of the reducibility of one problem to another and of a problem being complete for a class. Informally speaking, a problem \(X\) is said to be reducible to another problem \(Y\) just in case a method for solving \(Y\) would also yield a method for solving \(X\). The reducibility of \(X\) to \(Y\) may thus be understood as showing that solving \(Y\) is at least as difficult as solving \(X\). A problem \(X\) is said to be complete for a complexity class \(\textbf{C}\) just in case \(X\) is a member of \(\textbf{C}\) and all problems in \(\textbf{C}\) are reducible to \(X\). The completeness of \(X\) for \(\textbf{C}\) may thus be understood as demonstrating that \(X\) is representative of the most difficult problems in \(\textbf{C}\).