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
X Y X and Y X or Y X and Y X or Y
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.
X Y (X and Y) or (X and Y) (X or Y) and (X or Y) X or Y X or Y
0 0 0 1 1 1
0 1 1 0 1 0
1 0 1 0 0 1
1 1 0 1 1 1