Reasoning & Inequality Shortcuts

Rules for determining relationships without drawing scratch diagrams.

Operator Priority Hierarchy

1. Priority 1: > or <
2. Priority 2: >= or <=
3. Priority 3: =

Evaluation Axioms

• Unidirectional Path: If moving left to right and all operators point forward, the conclusion must contain the highest-priority operator present on that path.
• Opposing Signs: Any collision of opposing signs (> and <) immediately invalidates the direct relationship (Conclusion is False).