This Venn diagram is meant to represent a relation between

• two sets in set theory,
• or two statements in propositional logic respectively.

The relation 👁 Image
tells, that the set 👁 Image
is empty:   👁 Image
= 👁 Image

It can be written as 👁 {\displaystyle A\subseteq B^{c}}
or as 👁 {\displaystyle B\subseteq A^{c}}
.
It tells, that the sets 👁 {\displaystyle ~A}
and 👁 {\displaystyle ~B}
have no elements in common: 👁 {\displaystyle A\cap B=\emptyset }

Under this condition several set operations, not equivalent in general, produce equivalent results.
These equivalences define disjoint sets:

The sign 👁 {\displaystyle \Leftrightarrow }
tells, that two statements about sets mean the same.
The sign = tells, that two sets contain the same elements.

The relation 👁 Image
tells, that the statement 👁 Image
is never true:   👁 Image
👁 {\displaystyle \Leftrightarrow }
👁 Image

It can be written as 👁 {\displaystyle A\Rightarrow \neg B}
or as 👁 {\displaystyle B\Rightarrow \neg A}
.
It tells, that the statements 👁 {\displaystyle ~A}
and 👁 {\displaystyle ~B}
are never true together: 👁 {\displaystyle A\land B=false}

Under this condition several logic operations, not equivalent in general, produce equivalent results.
These equivalences define contrary statements:

The sign 👁 {\displaystyle \equiv }
tells, that two statements about statements about whatever objects mean the same.
The sign 👁 {\displaystyle \Leftrightarrow }
tells, that two statements about whatever objects mean the same.