1. The problem involves understanding the sample spaces of compound events when selecting cards labeled J, K, L, M. 2. Each set represents possible ordered pairs of outcomes from two draws or selections. 3. The first set includes all pairs from {J,K,L,M} with repetition allowed, so it has $4 \times 4 = 16$ outcomes. 4. The second set excludes pairs where the first and second letters are the same, so it has $4 \times 3 = 12$ outcomes. 5. The third set extends the sample space to include a fifth letter N, increasing the outcomes to $5 \times 5 = 25$. 6. The fourth set only includes pairs where both letters are the same, so it has 4 outcomes: {JJ, KK, LL, MM}. 7. Understanding these sample spaces helps in calculating probabilities of compound events in experiments with replacement or without replacement. Final answer: The sets represent different sample spaces for compound events with cards J, K, L, M (and N in one case), showing all pairs, pairs without repetition, extended pairs, and pairs with identical letters respectively.