Changes

{| align="center" cellpadding="8" width="90%"

{| align="center" cellpadding="8" width="90%"

| <math>P \times Q \ = \ P \times X \, \cap \, X \times Q.</math>

| <math>P \times Q \ = \ P \times X\ \cap\ X \times Q.</math>

|}

|}

From here it is easy to see the relation of concatenation, by virtue of these types of intersection, to the logical conjunction of propositions. The cartesian product <math>P \times Q</math> is described by a conjunction of propositions, namely, <math>P_1 \land Q_2,</math> subject to the following interpretation:

From here it is easy to see the relation of concatenation, by virtue of

these types of intersection, to the logical conjunction of propositions.

The cartesian product PxQ is described by a conjunction of propositions,

namely, "P_<1> and Q_<2>", subject to the following interpretation:

1.  "P_<1>" asserts that there is an element from

# <math>P_1\!</math> asserts that there is an element from the set <math>P\!</math> in the first place of the product.

    the set P in the first place of the product.

# <math>Q_2\!</math> asserts that there is an element from the set <math>Q\!</math> in the second place of the product.

The integration of these two pieces of information can be taken in that measure to specify a yet to be fully determined relation.

 

The integration of these two pieces of information can be taken

in that measure to specify a yet to be fully determined relation.

In a corresponding fashion at the level of the elements,

In a corresponding fashion at the level of the elements,

the ordered pair <p, q> is described by a conjunction

the ordered pair <p, q> is described by a conjunction