Venn Visualizer & Laws — A, B, C (∪ ∩ ′ \ −)
Union: ∪ (|, +), Intersection: ∩ (&, *), Complement: ′ (!, ~), Difference: \ or −
LHS diagram
RHS diagram
Read LHS: —
Read RHS: —
Equivalence: OK
| A | B | C | Region | LHS | RHS |
|---|
Identities Library (click to load both sides and verify)
(E′)′ = E Double complement
(A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C) Distributive
(A ∩ B) ∪ C = (A ∪ C) ∩ (B ∪ C) Distributive (other form)
(A ∪ B)′ = A′ ∩ B′ De Morgan
(A ∩ B)′ = A′ ∪ B′ De Morgan
A ∩ B = B ∩ A Commutative
A ∪ B = B ∪ A Commutative
How to read symbols
- A ∩ C: “A and C” (intersection).
- A ∪ B: “A or B” (union, at least one).
- A′: “not A” (complement, outside A).
- A \ B: “A minus B” (in A and not in B) — same as A ∩ B′.
- Precedence: complement (tightest), then ∩ and \, then ∪.