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Within this framework, the more complex strait <math>P \times Q</math> can be expressed  

Within this framework, the more complex strait PxQ can be expressed

in terms of the simpler straits, <math>P \times X</math> and <math>X \times Q.</math> More specifically, it lends itself to being analyzed as their intersection, in the following way:

in terms of the simpler straits, PxX and XxQ.  More specifically,

it lends itself to being analyzed as their intersection, in the

following way:

PxQ  = PxX |^| XxQ.

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

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

<pre>

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

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

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

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

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