The Subtraction Rule: Inclusion–Exclusion for Two Sets | Discrete Mathematics §6.1

When two ways of doing a task overlap, adding them double-counts the overlap. The fix is one of the most elegant ideas in counting: add, then subtract what you counted twice. In this video: the subtraction rule — the two-set case of inclusion–exclusion — built from a Venn diagram on the board. |A ∪ B| = |A| + |B| − |A ∩ B|. We apply it to bit strings that start or end a certain way, and to a small survey-style problem, and pull out the lesson: whenever your cases overlap, don't add blindly — subtract the intersection. This video is part of Discrete Mathematics · Counting (§6.1 — The Basics of Counting). Full section playlist → linked above / in the description on the channel. Made with the Engineering Simplified method: a calm, two-voice story lesson taught on a chalk-and-board, with every worked example written out step by step. Topic coverage follows Rosen, Discrete Mathematics and Its Applications (Chapter 6).