Chromium in the \( Cr^{2+} \) state has an electronic configuration of \( [Ar] 3d^4 \), which is relatively unstable and easily oxidizes to the more stable \( Cr^{3+} \) configuration, \( [Ar] 3d^5 \). This makes \( Cr^{2+} \) a strong reducing agent because it readily loses electrons. On the other hand, \( Mn^{3+} \) has an electronic configuration of \( [Ar] 3d^4 \), which is also unstable. It is prone to gaining electrons to become \( Mn^{2+} \), which has a more stable \( [Ar] 3d^5 \) configuration. Thus, \( Mn^{3+} \) is a strong oxidizing agent because it readily accepts electrons.
Thus, the differences in the electronic configurations of \( Cr^{2+} \) and \( Mn^{3+} \) explain why \( Cr^{2+} \) is a strong reducing agent and \( Mn^{3+} \) is a strong oxidizing agent.
A school is organizing a debate competition with participants as speakers and judges. $ S = \{S_1, S_2, S_3, S_4\} $ where $ S = \{S_1, S_2, S_3, S_4\} $ represents the set of speakers. The judges are represented by the set: $ J = \{J_1, J_2, J_3\} $ where $ J = \{J_1, J_2, J_3\} $ represents the set of judges. Each speaker can be assigned only one judge. Let $ R $ be a relation from set $ S $ to $ J $ defined as: $ R = \{(x, y) : \text{speaker } x \text{ is judged by judge } y, x \in S, y \in J\} $.