Final answer:
The question appears to misapply the term 'desire' where it likely meant to use 'set' or 'class' in the context of logical equivalence. A set of propositions is closed under logical equivalence if for any two propositions where one is logically equivalent to the other, both are within the set.
Step-by-step explanation:
The question "Is desire closed under logical equivalence?" seems to be a mix-up as 'desire' is not a mathematical term that can be closed under logical equivalence. Instead, it seems the proper term might be 'set' or 'class'. In mathematics, particularly in logic, logical equivalence refers to a relationship between statements that have the same truth value. The concept of being 'closed under an operation' typically applies to sets in the context of algebra or other branches of mathematics, meaning that applying the operation to elements of the set results in an element that is also within the set.
In the context of logical equivalence, if we are referring to a set of propositions, we say that the set is closed under logical equivalence if for any propositions P and Q in the set, if P is logically equivalent to Q, then Q is also in the set.