On the Subject of a Boolean Venn Diagram

Why is there a big Venn diagram? Why are there some weird symbols? Oh no...

See the original manual for the original instructions.

(A → B) | C
Action Effect
Click on an operator To change it
Click a section of a Venn diagram To mark it true or false
Two Diagrams:
Cheatsheet:
X Y
AND
X Y
OR
X Y
XOR
X Y
IMPLIES
X | Y
NAND
X Y
NOR
X ↔' Y
XNOR
X Y
IMPLIED BY
AND ∧ OR ∨ NAND | NOR ↓
A B A and B A or B A and B A or B
0 0 0 0 1 1
0 1 0 1 1 0
1 0 0 1 1 0
1 1 1 1 0 0

XOR ⊻ XNOR ↔ L. IMPL. → R. IMPL. ←
A B (A and B) or (A and B) (A or B) and (A or B) A or B A or B
0 0 0 1 1 1
0 1 1 0 1 0
1 0 1 0 0 1
1 1 0 1 1 1