Which of the following results in the best simplification? Note: Each circle is denoted by parenthesis. (A, B) indicates that a circle includes cells A and B.

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BlackTom AI · Accepted Answer

To determine the best simplification, start by understanding what each option represents in terms of grouping the items H, J, K, and L.
Option 1: '(H), (J), (K), (L)'. This splits every element into its own singleton circle. While valid, it is not the simplest grouping if we can combine elements into larger circles to reduce redundancy.
Option 2: '(H, J), (L, K)'. Here we create two circles, one containing H and J together, and another containing L and K together. This is a valid grouping, but it may not be the simplest if we can merge these groups further without losing correctness or increasing complexity.
Option 3: '(H, J), (L, K), (H, L), (J, K)'. This introduces more circles, including cross-relations like (H, L) and (J, K) in addition to the two initial pairs. The result is more complex than necessary because it adds extra groupings that are likely redundant for a simplification goal.
Option 4: '(H, J, K, L)'. This collapses all items into a single circle, representing the entire set as one group. In many simplification tasks, combining all elements into one circle is the most compact and simplest representation, as it communicates that all four items are included together in the same grouping without partitioning.
When evaluating simplifications, aim for the representation that minimizes the number of groupings while preserving the intended inclusion relationships. The first option over-fragments the set, the second option creates a partition into two groups that is not as minimal as possible, the third option adds unnecessary cross-relations, and the fourth option achieves the broadest, least redundant grouping by placing all items into one circle.
Thus, the fourth option achieves the best simplification by consolidating H, J, K, and L into a single circle, reducing complexity and conveying a unified group.

Which of the following results in the best simplification? Note: Each circle is denoted by parenthesis. (A, B) indicates that a circle includes cells A and B.

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