Classical propositional logic and set theory are often considered to be two instances of Boolean algebra, with set union corresponding to logical or, and set intersection corresponding to logical and. However, this does not reflect the logical structure of set theory. Thus, any set may be considered as the union of one-element sets, the sense of this representation depending on interpretation:

• Enumeration: the set is considered as element a and element b and element c and ... This is the simultaneous interpretation of set as an actual integrity - "strong" union.

• Exhausting: the set is considered as element a or element b or element c or ... This interpretation stresses the idea of potential integrity, referring to the operation of "probing" the set by random selection of one of the elements - "weak" union.

On the other hand, enumeration is algorithmic, in the sense that one is supposed to be able to construct the set being given its elements; the probing technique, inversely, refers to the quality of the set, the properties of the elements that makes them belong to the set.

Compare:

• the scheme of categorization by convention: "Let us refer to Mr. and Mrs. Jones as the Jones family."
• the scheme of explanation by example: "The vegetables are... well... the carrot, the cucumber, the onions, and like."

Also the two types of definition:

• by construction (explicit): "Numeric data types include integer, real, and date-time."
• by function (implicit): "Let all real numbers x<0 be called negative."