Venn Diagram Logic

Intro to Proofs · Axiom Academy

Two overlapping circles turn the abstract notation of set theory — union, intersection, complement — into a picture you can shade. The whole notation, as a picture Set theory is written in a terse symbolic shorthand — , , A' , — and at first those symbols are just marks on a page. A Venn diagram fixes that: two overlapping circles carve the world into regions, and every set operation becomes a specific patch you can point at and shade. Watch the shading sweep across the diagram as the operation on the left changes. Each operation lights up exactly the region it means: the union is everything inside either circle, the intersection only the overlap, the complement A' everything outside A , and the difference the part of A the overlap leaves behind. Same two circles every time — only the shaded patch changes. That patch is the operation. Pick an operation, see its region Tap each operation below and watch which region it shades. Notice how the picture decomposes the world into four atoms — only A , the overlap , only B , and outside both — and every operation is just some combination of those four. Read it the other way too: a shaded region you can see is a precise claim about which elements belong. Two expressions, one region: De Morgan's law

This is the written version of the interactive lesson above. See the full Intro to Proofs course.