The theorem in set theory and logic that for all sets 
and 
,
 |
(1)
|
where 
denotes complement set of 
and 
is the empty set. The
set 
is depicted in the above Venn diagram and clearly
coincides with 
iff 
is empty.
The corresponding theorem in a Boolean algebra 
states that for all elements 
of 
,
 |
(2)
|
The version of Poretsky's Law for logic can be derived from (2) using the rules of propositional calculus, namely for all propositions 
and 
,
![Q is equivalent to [(P and not Q) or (not P and Q)] iff P is false,](/images/equations/PoretskysLaw/NumberedEquation3.svg) |
(3)
|
where "is equivalent to" means having the same truth table. In fact, in the following table, the values in the second and in the third column coincide if and only if the value in the first column is 0.
 |  | ( and not  ) or (not  and  ) |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
