26.6 Compound Solution Verification

Compound Solution Verification is the process of confirming that a solved compound inequality, whether conjunctive or disjunctive, correctly represents its intended solution set by testing specific numerical values against the original, unsolved statement, extending the verification concepts used for single inequalities to account for the added complexity of two joined comparisons.

Connector Meaning Check is the first verification action, reviewing whether the compound inequality was correctly treated according to its actual connecting word, confirming that a statement joined by "and" was resolved using Simultaneous Truth Requirement and the techniques of Conjunctive Inequalities, or that a statement joined by "or" was resolved using At-Least-One Truth Requirement and the techniques of Disjunctive Inequalities, since applying the wrong standard to the wrong connector produces a fundamentally mismatched solution set.

Lower Boundary Test is the action of substituting the lower of the two boundary values obtained from solving into the original compound inequality, confirming that the resulting truth or falsity of the statement matches what the chosen Open Boundary Marker or Closed Boundary Marker at that position claims about its inclusion in the solution set.

Upper Boundary Test is the corresponding action performed at the higher of the two boundary values, confirming in the same manner that the resulting truth or falsity of the original statement matches the inclusion or exclusion indicated by the marker chosen for that boundary.

Interior Value Test is the action of selecting a specific numerical value from within the region claimed as part of the solution set, whether the Shared Solution Region of a conjunctive inequality or one of the Combined Outer Solution Regions of a disjunctive inequality, substituting it into the original compound statement, and confirming that it produces a true result, providing direct evidence that the claimed solution region is genuinely correct.

Exterior Value Test is the complementary action of selecting a specific numerical value from a region claimed to lie outside the solution set, such as the gap in a Disjoint Ray Result or the area beyond a Bounded Interval Result, substituting it into the original compound statement, and confirming that it produces a false result, providing evidence from the opposite direction that the boundaries of the solution region were correctly identified.

Compound Graph and Interval Agreement is the action of comparing every representation produced for the compound inequality, whether a Conjunctive Number-Line Region, a graphical depiction of a Disjoint Ray Result, a Conjunctive Interval Statement, or a Disjunctive Interval Union, confirming that each representation describes the identical set of values as every other, in fulfillment of the same standard established generally by Inequality Solution Representation Agreement.

Original Comparison Recheck is the concluding verification action, returning to the compound inequality exactly as it was originally presented, before any solving, simplification, or splitting into independent comparisons occurred, and confirming that every step taken, from Independent Comparison Resolution or Independent Disjunctive Resolution through the final combination of the two individual results, faithfully preserves the meaning of that original statement, closing the verification process with direct reference to the problem as first posed rather than to any intermediate transformed version of it.